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

`(x+3)` is a factor

Explanation:

Little Bézout's theorem states that the remainder of dividing a polynomial `p_n(x)` by a linear term `(x-a)`, is given by `p_n(a)`
Evaluating `p_3(x)=x^3-5x²-9x+45` for `x = -3` we have `p_3(-3)=0` then `(x+3)` is a factor of `p_3(x)`