# 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-3?

Jun 4, 2018

See below

#### Explanation:

The remainder theorem stablish that "the remainder of division of P(x) by x-a it's the same that P(a)". The consecuence is that (x-a) will be a factor of P(x).

Lets see:

Let be $P \left(x\right) = {x}^{3} - 5 {x}^{2} - 9 x + 45$

P(3)=3^3-5·3^2-9·3+45=0

So we can conclude by remainder theorem that $\left(x - 3\right)$ is a factor of $P \left(x\right)$