cum descompun un polinom in factori ireductibili?

Răspuns :

[tex]$ \ $ 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)[/tex]