Question

How do you use the factor theorem to determine whether x-3 is a factor of `2x^3-11x^2+12x+9`?

Answer 1

`x-a` is a factor of polynomial `P(x)` if and only if `P(a)=0`

Explanation:

`2(3)^3-11(3)^2+12(3)+9 = 54-99+36+9 = (54+36+9)-99 = 99-99=0`

So `x-3` is a factor of `2x^3-11x^2+12x+9`