# Find the rational roots of the polynomial and write the

Find the rational roots of the polynomial and write the polynomial P(x) factored if
$P\left(x\right)={x}^{3}-3x-2$
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alkaholikd9
Step 1
$P\left(x\right)={x}^{3}-3x-2$
${x}^{3}-3x-2=0$
${x}^{3}-4x+x-2=0$
$x\left({x}^{2}-4\right)+x-2=0$
x(x-2)(x+2)+x-2=0
Step 2
(x-2)(x(x+2)+1)=0
$\left(x-2\right)\left({x}^{2}+2x+1\right)=0$
(x-2)(x+1)^{2}=0
$x-2=0⇒x=2$
${\left(x+1\right)}^{2}=0⇒x=-1$
$\therefore$ The root are x=-1
and x=2
$\therefore P\left(x\right)=\left(x-2\right){\left(x+1\right)}^{2}$

twineg4