# How do you factor 4x^3+2x^2-2x-1?

Sep 1, 2016

$4 {x}^{3} + 2 {x}^{2} - 2 x - 1 = \left(\sqrt{2} x - 1\right) \left(\sqrt{2} x + 1\right) \left(2 x + 1\right)$

#### Explanation:

Notice that the ratio of the first and second terms is the same as that of the third and fourth terms. So this cubic will factor by grouping:

$4 {x}^{3} + 2 {x}^{2} - 2 x - 1$

$= \left(4 {x}^{3} + 2 {x}^{2}\right) - \left(2 x + 1\right)$

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

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

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

$= \left(\sqrt{2} x - 1\right) \left(\sqrt{2} x + 1\right) \left(2 x + 1\right)$