Question

Find the value of a, if $\text{x}\text{-}\text{a}$ is factor of $x^3-a^{2}x+x+2$.

Answer 1

We have,

$p\left(x\right)=x^3-a^{2}x+x+2$

Since, $(x-a)$ is the factor of this polynomial.

So,

$p\left(a\right)=0$

Therefore,

$a^3-a^2\left(a\right)+a+2=0$

$a^3-a^3+a+2=0$

$a+2=0$

$a=-2$

Hence, this is the answer.