Question

If $x+1$ is a factor of $a{x}^3+x^2-2x+4a-9,$ find the value of $a$.

• A. $2$
• B. $1$
• C. $0$
• D. $3$

Answer 1

The correct option is A $2$

Let $p\left(x\right)=a{x}^3+x^2-2x+4a-9$ and $g\left(x\right)=x+1$

Now,
$x+1=0$
$\Rightarrow x=-1$

By using factor theorem, if $g\left(x\right)$ is a factor of $p\left(x\right)$, then $p(-1)$ must be $0.$

Thus,

$p(-1)=0$
$\Rightarrow a(-1{)}^3+(-1{)}^2-2(-1)+4a-9=0$
$\Rightarrow -a+1+2+4a-9=0$
$\Rightarrow 3a-6=0$
$\Rightarrow a=2$