# How do you factor given that f(-5)=0 and f(x)=4x^3+9x^2-52x+15?

We know that $- 5$ is a factor by the remainder theorem. We divide $4 {x}^{3} + 9 {x}^{2} - 52 x + 15$ by $x + 5$:
So, our current factoring is $\left(x + 5\right) \left(4 {x}^{2} - 11 x + 3\right)$.
$4 {x}^{2} - 11 x + 3$ cannot be factored any further, so this is as far as we can go.