# How do you completely factor x^3+9x^2+12x+15 given x+5 is one of the factors?

Sep 27, 2016

Let, $p \left(x\right) = {x}^{3} + 9 {x}^{2} + 12 x + 15$, and, we are given that $\left(x + 5\right)$

is a factor of $p \left(x\right)$.

But, this is not true , because,

$p \left(- 5\right) = - 125 + 225 - 60 + 15 = 55 \ne 0$

#### Explanation:

Let, $p \left(x\right) = {x}^{3} + 9 {x}^{2} + 12 x + 15$, and, we are given that $\left(x + 5\right)$

is a factor of $p \left(x\right)$.

But, this is not true , because,

$p \left(- 5\right) = - 125 + 225 - 60 + 15 = 55 \ne 0$