Question

Find 'a', if$x+1$ is a factor of $x^3+{3x}^2-2ax.$

Answer 1

If $(x+1)$ is a factor of $p\left(x\right)$. Then $p(-1)=0$

$p\left(x\right)=x^3+3x^2-2ax$

$p(-1)=(-1{)}^3+3(-1{)}^2-2a(-1)=0$

$=-1+3+2a=0$

$\Rightarrow 2+2a=0$

$\Rightarrow a=\frac{-2}{2}=-1$.