# How do you factor 4x^3-28x^2-x+7?

Jun 12, 2016

$= \left(x - 7\right) \left(2 x + 1\right) \left(2 x - 1\right)$

#### Explanation:

As soon as there are 4 terms, group them together in pairs first - making sure there is a PLUS sign between the pairs.
Choose the pairs so that they can be factorised further.
$\left(4 {x}^{3} - {28}^{2}\right) + \left(- x + 7\right)$

$= 4 {x}^{2} \left(x - 7\right) - \left(x - 7\right) \text{ common factors }$

$= \left(x - 7\right) \left(4 {x}^{2} - 1\right) \text{ Diff of squares}$

$= \left(x - 7\right) \left(2 x + 1\right) \left(2 x - 1\right)$