Question

cum descompun un polinom in factori ireductibili?

Answer 1

$\ Un polinom F = a_n x ^n + a_{(n-1)} x ^{n-1}+a_{(n-2)} x ^{n-2}} +...+a_1 x ^1+a_0 x ^0 \\ \\ Are radaciniile x _1, x _2, x _3,.., x _n Iar el poate fi scris in factori ireductibili ca: \\ F = a_n\cdot( x - x _1)\cdot( x - x _2)\cdot( x - x _3)\cdot...\cdot( x - x _n) \\ \\ Luam un exemplu: F = x ^3-3 x +2 \\ \ -are radacinile x _1 =1, x _2=1, x _3 = -2 \\ - a_n = 1 \\ \\ \Rightarrow F = 1\cdot( x -1)\cdot( x -1)\cdot( x -\big(-2)\big) \Rightarrow F = ( x -1)^2\cdot( x +2)$