Question

Check whether, $x-2$ is a factor of the polynomial $x^3-x^2-4$ by using factor theorem.

Answer 1

According to factor theorem for

$f\left(x\right)=x^3-x^2-4$ to have $x-2$ as its factor $f\left(2\right)$ should be equal to zero

$f\left(2\right)=(2{)}^3-(2{)}^2-4$

$=8-4-4$

$=0$

So, $x-2$ is a factor of $f\left(x\right)$