Question

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`?

Answer 1

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(x)=x^3-5x^2-9x+45`

`P(3)=3^3-5·3^2-9·3+45=0`

So we can conclude by remainder theorem that `(x-3)` is a factor of `P(x)`