# How do you factor 12a^3+2a^2-192a-32?

Apr 17, 2018

The fully factored form is $2 \left(a - 4\right) \left(a + 4\right) \left(6 a + 1\right)$.

#### Explanation:

Use the factor by grouping method:

$\textcolor{w h i t e}{=} 12 {a}^{3} + 2 {a}^{2} - 192 a - 32$

$= 2 {a}^{2} \left(6 a + 1\right) - 192 a - 32$

$= 2 {a}^{2} \left(6 a + 1\right) - 32 \left(6 a + 1\right)$

$= \left(2 {a}^{2} - 32\right) \left(6 a + 1\right)$

$= 2 \left({a}^{2} - 16\right) \left(6 a + 1\right)$

$= 2 \left(a - 4\right) \left(a + 4\right) \left(6 a + 1\right)$

That's the fully factored form. Hope this helped!