# How do you use the remainder theorem to find which if the following is not a factor of the polynomial x^3-5x^2-9x+45 div x+5?

The remainder is $= - 160$, so $\left(x + 5\right)$ is not a factor
Let $f \left(x\right) = {x}^{3} - 5 {x}^{2} - 9 x + 45$
then $f \left(- 5\right) = - 125 - 125 + 45 + 45 = - 160$
The remaider is $= - 160$
$\therefore$ $\left(x + 5\right)$ is not a factor of ${x}^{3} - 5 {x}^{2} - 9 x + 45$