Question

Find the value of $P$ such that $(x-1)$ is a factor of the polynomial $x^3+10x^2+px$.

Answer 1

If $x-1$ is a factor of $f\left(x\right)$, then 1 shoud be a zero of $f\left(x\right)$ {Factor theorem}

$\Rightarrow f\left(1\right)=0\Rightarrow 1+10+P=0\Rightarrow P=-11$