<prompt> Hebu Px 0 kuwa polynomial equation ya kiwango cha chini iwezekanavyo, na coefficients rational, kuwa 713 4913 kama mzizi. Mahesabu ya bidhaa ya mizizi yote ya Px 0.  <response>: Tunatambua idadi 713 4913 kutoka tofauti-ya-makubu factorization 7 - 1 713 - 1 1 713 4913. kutatua kwa 713 4913, tunapata 713 4913 7-1 7713 - 1 6713 - 1. Tunaweza kutumia usemi huu kujenga polynomial ambayo ina 713 4913 kama mzizi. Kwanza, kumbuka kwamba 713 ni mzizi wa x3 - 7 0., basi 71-13 ni mzizi wa pande x3 1 - 7 0. kwa sababu 713 4913 - 713, tunapata 713 4913 0. - Mwishowe tunaweza kuona kwamba mzizi wa x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 