# How do you factor 4x^3+13x^2-13x-4 ?

##### 1 Answer
Jun 8, 2015

Notice that the sum of the coefficients is zero, so $1$ is a zero:

$f \left(x\right) = 4 {x}^{3} + 13 {x}^{2} - 13 x - 4$

$f \left(1\right) = 4 + 13 - 13 - 4 = 0$

So $\left(x - 1\right)$ is a factor.

$f \left(x\right) = \left(x - 1\right) \left(4 {x}^{2} + 17 x + 4\right)$

$= \left(x - 1\right) \left(4 {x}^{2} + 1 x + 16 x + 4\right)$

$= \left(x - 1\right) \left(x \cdot \left(4 x + 1\right) + 4 \cdot \left(4 x + 1\right)\right)$

$= \left(x - 1\right) \left(x + 4\right) \left(4 x + 1\right)$