144:@0.052592:0.966074:0.080768:0.966074:0.080768:0.949450:0.052592:0.949450:0.000000:0.000000:0.000000
Tema 3:@0.124729:0.083964:0.219414:0.083964:0.219414:0.055923:0.124729:0.055923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Descomposición factorial: factor común:@0.305293:0.083059:0.821348:0.083059:0.821348:0.055403:0.305293:0.055403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Factorizar se refiere a la descomposición de un polinomio en el producto de otros :@0.304744:0.235083:0.907123:0.235083:0.907123:0.219413:0.304744:0.219413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
polinomios de grado inferior al dado.:@0.304744:0.251679:0.575663:0.251679:0.575663:0.236009:0.304744:0.236009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Existen varias técnicas de factorización, y en este tema vamos a tratar la factoriza-:@0.304744:0.275398:0.903010:0.275398:0.903010:0.259728:0.304744:0.259728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción de un polinomio por factor común.:@0.304744:0.291994:0.599324:0.291994:0.599324:0.276325:0.304744:0.276325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Algunas de las expresiones matemáticas que modelan el movimiento de las ondas :@0.304744:0.315713:0.907198:0.315713:0.907198:0.300044:0.304744:0.300044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que transportan energía son::@0.304744:0.332310:0.516510:0.332310:0.516510:0.316640:0.304744:0.316640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.304744:0.356029:0.308779:0.356029:0.308779:0.340359:0.304744:0.340359:0.000000
A sen t:@0.365209:0.355684:0.432835:0.355684:0.438055:0.340014:0.370429:0.340014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( (:@0.410126:0.355685:0.415769:0.356045:0.415769:0.340375:0.410126:0.340016:0.000000:0.000000:0.000000
) ):@0.437401:0.355685:0.439600:0.356045:0.439600:0.340375:0.437401:0.340016:0.000000:0.000000:0.000000
ω:@0.413812:0.356584:0.426453:0.356584:0.431640:0.341011:0.418999:0.341011:0.000000
t:@0.429336:0.356045:0.434717:0.356045:0.434717:0.339684:0.429336:0.339684:0.000000
A:@0.608119:0.356044:0.618899:0.356044:0.624119:0.340374:0.613338:0.340374:0.000000
cos((:@0.627907:0.356045:0.657970:0.356045:0.657970:0.340375:0.627907:0.340375:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.669056:0.356044:0.674750:0.356044:0.679969:0.340374:0.674275:0.340374:0.000000
) ):@0.679317:0.356045:0.681802:0.356045:0.681802:0.340375:0.679317:0.340375:0.000000:0.000000:0.000000
ω:@0.656013:0.356584:0.668654:0.356584:0.673841:0.341011:0.661200:0.341011:0.000000
t:@0.671537:0.356045:0.676918:0.356045:0.676918:0.339684:0.671537:0.339684:0.000000
Si   es un factor, :@0.304735:0.383540:0.432142:0.383540:0.432142:0.367870:0.304735:0.367870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.322334:0.383540:0.332229:0.383540:0.332229:0.367178:0.322334:0.367178:0.000000
sen t:@0.432669:0.383540:0.482077:0.383540:0.487297:0.367870:0.437889:0.367870:0.000000:0.000000:0.000000:0.000000:0.000000
((:@0.459368:0.383541:0.464972:0.383541:0.464972:0.367871:0.459368:0.367871:0.000000:0.000000
) ) es otro factor y cos((:@0.486643:0.383541:0.643345:0.383541:0.643345:0.367871:0.486643:0.367871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ω:@0.463015:0.384080:0.475656:0.384080:0.480844:0.368507:0.468202:0.368507:0.000000
t:@0.478540:0.383541:0.483921:0.383541:0.483921:0.367180:0.478540:0.367180:0.000000
 :@0.606464:0.388575:0.610500:0.388575:0.610500:0.372905:0.606464:0.372905:0.000000
t:@0.655429:0.383540:0.661123:0.383540:0.666343:0.367870:0.660649:0.367870:0.000000
) ) es otro factor, ¿cuál es el factor :@0.665689:0.383541:0.907138:0.383541:0.907138:0.367871:0.665689:0.367871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ω:@0.641386:0.384080:0.654027:0.384080:0.659215:0.368507:0.646574:0.368507:0.000000
t:@0.656911:0.383541:0.662292:0.383541:0.662292:0.367180:0.656911:0.367180:0.000000
común que tienen estas dos expresiones?:@0.304740:0.400137:0.611444:0.400137:0.611444:0.384468:0.304740:0.384468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Al comparar las dos expresiones, observamos que el factor común es  .:@0.304740:0.423856:0.826880:0.423856:0.826880:0.408187:0.304740:0.408187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.813778:0.423856:0.823674:0.423856:0.823674:0.407495:0.813778:0.407495:0.000000
Factorización de monomios:@0.319266:0.476238:0.538611:0.476238:0.538611:0.459337:0.319266:0.459337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Factorizar un monomio significa expresarlo como el producto de otros :@0.315913:0.499957:0.894575:0.499957:0.894575:0.484287:0.315913:0.484287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.890523:0.499957:0.894559:0.499957:0.894559:0.484287:0.890523:0.484287:0.000000
monomios. :@0.315913:0.516553:0.403149:0.516553:0.403149:0.500884:0.315913:0.500884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 1:@0.304744:0.564078:0.374249:0.564078:0.374249:0.548965:0.304744:0.548965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.374248:0.564392:0.378283:0.564392:0.378283:0.548723:0.374248:0.548723:0.000000
Factorizar el monomio  6:@0.425366:0.564392:0.617183:0.564341:0.617183:0.548671:0.425366:0.548723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
xy:@0.616705:0.564341:0.641822:0.564341:0.646415:0.548671:0.621298:0.548671:0.000000:0.000000
3:@0.628346:0.556680:0.633558:0.556680:0.633558:0.547598:0.628346:0.547598:0.000000
2:@0.646149:0.556680:0.651361:0.556680:0.651361:0.547598:0.646149:0.547598:0.000000
−:@0.594108:0.565018:0.604225:0.565018:0.604225:0.549446:0.594108:0.549446:0.000000
Solución  :@0.304744:0.589941:0.372507:0.589941:0.372507:0.574828:0.304744:0.574828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una de las tantas formas puede ser: 23:@0.425361:0.590255:0.725916:0.590840:0.725916:0.575170:0.425361:0.574585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.685227:0.595289:0.689263:0.595289:0.689263:0.579620:0.685227:0.579620:0.000000
−⋅ ⋅:@0.690429:0.591517:0.731689:0.591517:0.731689:0.575944:0.690429:0.575944:0.000000:0.000000:0.000000:0.000000
⋅⋅⋅:@0.752361:0.591517:0.792976:0.591517:0.792976:0.575944:0.752361:0.575944:0.000000:0.000000:0.000000
xx yy:@0.734508:0.590840:0.803288:0.590840:0.803288:0.574478:0.734508:0.574478:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.743618:0.583177:0.748830:0.583177:0.748830:0.574096:0.743618:0.574096:0.000000
 :@0.804392:0.590255:0.808428:0.590255:0.808428:0.574585:0.804392:0.574585:0.000000
Factorización de polinomios que tienen un factor común:@0.319266:0.639080:0.767548:0.639080:0.767548:0.622179:0.319266:0.622179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El factor común de un polinomio se forma con el m.c.d. de los coeficientes y las :@0.315913:0.662799:0.894614:0.662799:0.894614:0.647129:0.315913:0.647129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
letras de la parte literal que sean comunes con el menor exponente. Una vez :@0.315913:0.679395:0.894596:0.679395:0.894596:0.663725:0.315913:0.663725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conformado el factor común, dividimos cada término del polinomio para el :@0.315913:0.695992:0.894575:0.695992:0.894575:0.680322:0.315913:0.680322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
factor común. Los cocientes constituyen el polinomio factor.:@0.315913:0.712588:0.757910:0.712588:0.757910:0.696918:0.315913:0.696918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 2:@0.304744:0.763822:0.374249:0.763822:0.374249:0.748709:0.304744:0.748709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Factorizar el monomio  4:@0.304744:0.790375:0.485780:0.790375:0.485780:0.774705:0.304744:0.774705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.535535:0.791052:0.545652:0.791052:0.545652:0.775479:0.535535:0.775479:0.000000
+:@0.614055:0.791052:0.624172:0.791052:0.624172:0.775479:0.614055:0.775479:0.000000
ab c:@0.486683:0.790375:0.525178:0.790375:0.525178:0.774013:0.486683:0.774013:0.000000:0.000000:0.000000:0.000000
a bc:@0.565203:0.790375:0.603699:0.790375:0.603699:0.774013:0.565203:0.774013:0.000000:0.000000:0.000000:0.000000
abc:@0.645253:0.790375:0.677262:0.790375:0.677262:0.774013:0.645253:0.774013:0.000000:0.000000:0.000000
12:@0.547255:0.790375:0.565037:0.790375:0.565037:0.774705:0.547255:0.774705:0.000000:0.000000
20:@0.626936:0.790375:0.644719:0.790375:0.644719:0.774705:0.626936:0.774705:0.000000:0.000000
23 5:@0.496534:0.782714:0.531424:0.782714:0.531424:0.773632:0.496534:0.773632:0.000000:0.000000:0.000000:0.000000
3 23:@0.575061:0.782714:0.609951:0.782714:0.609951:0.773632:0.575061:0.773632:0.000000:0.000000:0.000000:0.000000
5:@0.655105:0.782714:0.660317:0.782714:0.660317:0.773632:0.655105:0.773632:0.000000
2:@0.678301:0.782714:0.683513:0.782714:0.683513:0.773632:0.678301:0.773632:0.000000
Solución:@0.304744:0.818771:0.365404:0.818771:0.365404:0.803658:0.304744:0.803658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La m.c.d. de 4, 12 y 20 es 4. :@0.304744:0.842809:0.503486:0.842809:0.503486:0.827139:0.304744:0.827139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la parte literal común es :@0.304744:0.869045:0.507243:0.869045:0.507243:0.853375:0.304744:0.853375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
abc:@0.510225:0.869049:0.542437:0.869049:0.542437:0.852688:0.510225:0.852688:0.000000:0.000000:0.000000
2:@0.520067:0.861387:0.525279:0.861387:0.525279:0.852305:0.520067:0.852305:0.000000
2:@0.543466:0.861387:0.548678:0.861387:0.548678:0.852305:0.543466:0.852305:0.000000
. Por lo tanto, el factor común es  4:@0.549686:0.869049:0.801307:0.869049:0.801307:0.853379:0.549686:0.853379:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
abc:@0.802209:0.869049:0.834421:0.869049:0.834421:0.852688:0.802209:0.852688:0.000000:0.000000:0.000000
2:@0.812052:0.861387:0.817263:0.861387:0.817263:0.852305:0.812052:0.852305:0.000000
2:@0.835451:0.861387:0.840662:0.861387:0.840662:0.852305:0.835451:0.852305:0.000000
. :@0.841244:0.869049:0.848486:0.869049:0.848486:0.853379:0.841244:0.853379:0.000000:0.000000
Dividimos cada término del polinomio para el factor común y obtenemos::@0.304742:0.892768:0.848204:0.892768:0.848204:0.877098:0.304742:0.877098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.366831:0.918432:0.376948:0.918432:0.376948:0.902859:0.366831:0.902859:0.000000
+:@0.445352:0.918432:0.455468:0.918432:0.455468:0.902859:0.445352:0.902859:0.000000
ab c:@0.317980:0.917755:0.356475:0.917755:0.356475:0.901393:0.317980:0.901393:0.000000:0.000000:0.000000:0.000000
a bc:@0.396500:0.917755:0.434995:0.917755:0.434995:0.901393:0.396500:0.901393:0.000000:0.000000:0.000000:0.000000
abc:@0.476550:0.917755:0.508558:0.917755:0.508558:0.901393:0.476550:0.901393:0.000000:0.000000:0.000000
4:@0.308084:0.917755:0.317077:0.917755:0.317077:0.902085:0.308084:0.902085:0.000000
12:@0.378551:0.917755:0.396334:0.917755:0.396334:0.902085:0.378551:0.902085:0.000000:0.000000
20:@0.458233:0.917755:0.476015:0.917755:0.476015:0.902085:0.458233:0.902085:0.000000:0.000000
23 5:@0.327830:0.910093:0.362721:0.910093:0.362721:0.901012:0.327830:0.901012:0.000000:0.000000:0.000000:0.000000
3 23:@0.406358:0.910093:0.441248:0.910093:0.441248:0.901012:0.406358:0.901012:0.000000:0.000000:0.000000:0.000000
5:@0.486402:0.910093:0.491613:0.910093:0.491613:0.901012:0.486402:0.901012:0.000000
2:@0.509598:0.910093:0.514810:0.910093:0.514810:0.901012:0.509598:0.901012:0.000000
 =  4:@0.516497:0.916497:0.547893:0.917755:0.547893:0.902085:0.516497:0.900828:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.628003:0.918432:0.638120:0.918432:0.638120:0.902859:0.628003:0.902859:0.000000
+:@0.678992:0.918432:0.689109:0.918432:0.689109:0.902859:0.678992:0.902859:0.000000
abcb c:@0.548796:0.917755:0.617660:0.917755:0.617660:0.901393:0.548796:0.901393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
abc:@0.649632:0.917755:0.675726:0.917755:0.675726:0.901393:0.649632:0.901393:0.000000:0.000000:0.000000
a:@0.700621:0.917755:0.709890:0.917755:0.709890:0.901393:0.700621:0.901393:0.000000
(:@0.588581:0.917755:0.593465:0.917755:0.593465:0.902085:0.588581:0.902085:0.000000
3:@0.640882:0.917755:0.649875:0.917755:0.649875:0.902085:0.640882:0.902085:0.000000
5 ):@0.691871:0.917755:0.722827:0.917755:0.722827:0.902085:0.691871:0.902085:0.000000:0.000000:0.000000
2:@0.558638:0.910093:0.563850:0.910093:0.563850:0.901012:0.558638:0.901012:0.000000
2:@0.582037:0.910093:0.587249:0.910093:0.587249:0.901012:0.582037:0.901012:0.000000
23:@0.604133:0.910093:0.623901:0.910093:0.623901:0.901012:0.604133:0.901012:0.000000:0.000000
3:@0.710460:0.910093:0.715672:0.910093:0.715672:0.901012:0.710460:0.901012:0.000000
Efectúa:@0.311168:0.162422:0.370653:0.162422:0.370653:0.145521:0.311168:0.145521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 los productos en tu cuaderno.:@0.370653:0.162422:0.594858:0.162422:0.594858:0.146752:0.370653:0.146752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
++:@0.341793:0.188082:0.377617:0.188082:0.377617:0.172509:0.341793:0.172509:0.000000:0.000000
ax yz:@0.314152:0.187404:0.388710:0.187404:0.388710:0.171043:0.314152:0.171043:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.323255:0.187404:0.328138:0.187404:0.328138:0.171735:0.323255:0.171735:0.000000
):@0.390571:0.187404:0.395455:0.187404:0.395455:0.171735:0.390571:0.171735:0.000000
−:@0.499323:0.188082:0.509440:0.188082:0.509440:0.172509:0.499323:0.172509:0.000000
xy:@0.440317:0.187404:0.455078:0.187404:0.455078:0.171043:0.440317:0.171043:0.000000:0.000000
xy:@0.480674:0.187404:0.495435:0.187404:0.495435:0.171043:0.480674:0.171043:0.000000:0.000000
x:@0.522026:0.187404:0.529489:0.187404:0.529489:0.171043:0.522026:0.171043:0.000000
2:@0.430053:0.187404:0.439046:0.187404:0.439046:0.171735:0.430053:0.171735:0.000000
(4:@0.463241:0.187404:0.478684:0.187404:0.478684:0.171735:0.463241:0.171735:0.000000:0.000000
5:@0.512204:0.187404:0.521196:0.187404:0.521196:0.171735:0.512204:0.171735:0.000000
y):@0.539999:0.187404:0.561486:0.187404:0.561486:0.171735:0.539999:0.171735:0.000000:0.000000
2:@0.456708:0.179742:0.461920:0.179742:0.461920:0.170661:0.456708:0.170661:0.000000
2:@0.531156:0.179742:0.536368:0.179742:0.536368:0.170661:0.531156:0.170661:0.000000
3:@0.549108:0.179742:0.554319:0.179742:0.554319:0.170661:0.549108:0.170661:0.000000
 :@0.564813:0.193691:0.568849:0.193691:0.568849:0.178021:0.564813:0.178021:0.000000
+:@0.604597:0.188082:0.555395:0.188082:0.555395:0.172509:0.604597:0.172509:0.000000
+:@0.663915:0.188082:0.614713:0.188082:0.614713:0.172509:0.663915:0.172509:0.000000
az:@0.592508:0.187404:0.625825:0.187404:0.625825:0.171043:0.592508:0.171043:0.000000:0.000000
m:@0.646796:0.187404:0.661427:0.187404:0.661427:0.171043:0.646796:0.171043:0.000000
p:@0.686268:0.187404:0.695537:0.187404:0.695537:0.171043:0.686268:0.171043:0.000000
(:@0.586427:0.187404:0.591310:0.187404:0.591310:0.171735:0.586427:0.171735:0.000000
)(2:@0.627686:0.187404:0.646999:0.187404:0.646999:0.171735:0.627686:0.171735:0.000000:0.000000:0.000000
3):@0.676796:0.187404:0.701415:0.187404:0.701415:0.171735:0.676796:0.171735:0.000000:0.000000
 :@0.704850:0.193691:0.708885:0.193691:0.708885:0.178021:0.704850:0.178021:0.000000
+:@0.764373:0.188082:0.774489:0.188082:0.774489:0.172509:0.764373:0.172509:0.000000
−:@0.829385:0.188082:0.839502:0.188082:0.839502:0.172509:0.829385:0.172509:0.000000
w:@0.776831:0.187404:0.789565:0.187404:0.789565:0.171043:0.776831:0.171043:0.000000
x:@0.810757:0.187404:0.818220:0.187404:0.818220:0.171043:0.810757:0.171043:0.000000
y:@0.852532:0.187404:0.860014:0.187404:0.860014:0.171043:0.852532:0.171043:0.000000
(7y:@0.738870:0.187404:0.763305:0.187404:0.763305:0.171735:0.738870:0.171735:0.000000:0.000000:0.000000
)(:@0.798963:0.187404:0.808466:0.187404:0.808466:0.171735:0.798963:0.171735:0.000000:0.000000
2 ):@0.842263:0.187404:0.866942:0.187404:0.866942:0.171735:0.842263:0.171735:0.000000:0.000000:0.000000
2:@0.791280:0.179742:0.796492:0.179742:0.796492:0.170661:0.791280:0.170661:0.000000
2:@0.819870:0.179742:0.825081:0.179742:0.825081:0.170661:0.819870:0.170661:0.000000
Saberes previos:@0.344861:0.135794:0.470369:0.135794:0.470369:0.118893:0.344861:0.118893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Modelación de expresiones :@0.096359:0.326207:0.264694:0.326207:0.264694:0.313386:0.096359:0.313386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
algebraicas:@0.096359:0.339786:0.163875:0.339786:0.163875:0.326965:0.096359:0.326965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.089444:0.263793:0.094176:0.263793:0.094176:0.255473:0.089444:0.255473:0.000000
A:@0.121817:0.233413:0.126769:0.233413:0.126769:0.225709:0.121817:0.225709:0.000000
 :@0.126769:0.233413:0.128724:0.233413:0.128724:0.225093:0.126769:0.225093:0.000000
sen :@0.128724:0.233413:0.144071:0.233413:0.144071:0.225093:0.128724:0.225093:0.000000:0.000000:0.000000:0.000000
   :@0.144071:0.233752:0.150988:0.233752:0.150988:0.225958:0.144071:0.225958:0.000000:0.000000:0.000000
t:@0.150988:0.233413:0.153681:0.233413:0.153681:0.225709:0.150988:0.225709:0.000000
A:@0.127645:0.248842:0.132598:0.248842:0.132598:0.241138:0.127645:0.241138:0.000000
 :@0.132598:0.248842:0.134553:0.248842:0.134553:0.240522:0.132598:0.240522:0.000000
cos :@0.134553:0.248842:0.149301:0.248842:0.149301:0.240522:0.134553:0.240522:0.000000:0.000000:0.000000:0.000000
   :@0.149301:0.249181:0.156218:0.249181:0.156218:0.241387:0.149301:0.241387:0.000000:0.000000:0.000000
t:@0.156218:0.248842:0.158911:0.248842:0.158911:0.241138:0.156218:0.241138:0.000000
ω:@0.144212:0.233205:0.150012:0.233205:0.152392:0.226061:0.146592:0.226061:0.000000
ω:@0.149377:0.249073:0.155176:0.249073:0.157556:0.241928:0.151756:0.241928:0.000000
Como la energía viaja :@0.104854:0.423492:0.251654:0.423492:0.251654:0.409246:0.104854:0.409246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en forma de ondas, :@0.104854:0.438579:0.236895:0.438579:0.236895:0.424334:0.104854:0.424334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la matemática ha :@0.104854:0.453667:0.223208:0.453667:0.223208:0.439422:0.104854:0.439422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conseguido modelar :@0.104854:0.468754:0.247434:0.468754:0.247434:0.454509:0.104854:0.454509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
este movimiento con :@0.104854:0.483842:0.250732:0.483842:0.250732:0.469597:0.104854:0.469597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expresiones algebraicas :@0.104854:0.498930:0.266665:0.498930:0.266665:0.484685:0.104854:0.484685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que muestran el :@0.104854:0.514017:0.217330:0.514017:0.217330:0.499772:0.104854:0.499772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tamaño de la onda y la :@0.104854:0.529105:0.260400:0.529105:0.260400:0.514860:0.104854:0.514860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
frecuencia con que se :@0.104854:0.544193:0.254688:0.544193:0.254688:0.529947:0.104854:0.529947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producen.:@0.104854:0.559280:0.173271:0.559280:0.173271:0.545035:0.104854:0.545035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.140215:0.387921:0.250520:0.387921:0.250520:0.369620:0.140215:0.369620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.140215:0.400489:0.236246:0.400489:0.236246:0.382188:0.140215:0.382188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La práctica de conteo, :@0.106105:0.662202:0.256422:0.662202:0.256422:0.647956:0.106105:0.647956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vigente en algunas :@0.106105:0.677289:0.236707:0.677289:0.236707:0.663044:0.106105:0.663044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
zonas de los Andes, :@0.106105:0.692377:0.240089:0.692377:0.240089:0.678132:0.106105:0.678132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tiene relación con sus :@0.106105:0.707464:0.254347:0.707464:0.254347:0.693219:0.106105:0.693219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
creencias. Por ejemplo, :@0.106105:0.722552:0.261833:0.722552:0.261833:0.708307:0.106105:0.708307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el resultado del conteo :@0.106105:0.737640:0.263107:0.737640:0.263107:0.723394:0.106105:0.723394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de semillas significa que :@0.106105:0.752727:0.270963:0.752727:0.270963:0.738482:0.106105:0.738482:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tendrán abundancia :@0.106105:0.767815:0.245267:0.767815:0.245267:0.753570:0.106105:0.753570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o deficiencia de :@0.106105:0.782902:0.215263:0.782902:0.215263:0.768657:0.106105:0.768657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producción en la :@0.106105:0.797990:0.222634:0.797990:0.222634:0.783745:0.106105:0.783745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
agricultura, según se :@0.106105:0.813078:0.247445:0.813078:0.247445:0.798832:0.106105:0.798832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
obtenga una cantidad :@0.106105:0.828165:0.258217:0.828165:0.258217:0.813920:0.106105:0.813920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
par o impar.:@0.106105:0.843253:0.185325:0.843253:0.185325:0.829008:0.106105:0.829008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interculturalidad:@0.136439:0.636441:0.266163:0.636441:0.266163:0.618139:0.136439:0.618139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.1.:@0.096359:0.939935:0.135984:0.939935:0.135984:0.929180:0.096359:0.929180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Aplicar las propiedades algebraicas de los números reales en la resolución de productos notables y en la factorización de expresiones algebraicas.:@0.135984:0.939935:0.815396:0.939935:0.815396:0.929963:0.135984:0.929963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000