Question

Check whether the following polynomial has $(x+1)$ as a factor.
$x^3-x^2-x+1$

Answer 1

To check whether $(x+1)$ is the factor of polynomial $x^3-x^2-x+1$

Then $x+1=0$ or $x=-1$

Replace $x$ by $-1$ we get

$P\left(x\right)=x^3-x^2-x+1$

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

$p(-1)=-1-1+1+1$

$p(-1)=0$

Value of $p(-1)$ is zero $⟹x+1$ is the factor of polynomial $x^3-x^2-x+1$