# How do you factor the expression 14x^3 - 21x^2 - 2x + 3?

Dec 29, 2015

Factor by grouping then using the difference of squares identity to find:

$14 {x}^{3} - 21 {x}^{2} - 2 x + 3$

$= \left(7 {x}^{2} - 1\right) \left(2 x - 3\right)$

$= \left(\sqrt{7} x - 1\right) \left(\sqrt{7} x + 1\right) \left(2 x - 3\right)$

#### Explanation:

The difference of squares identity can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Use this with $a = \sqrt{7} x$ and $b = 1$ to find:

$14 {x}^{3} - 21 {x}^{2} - 2 x + 3$

$= \left(14 {x}^{3} - 21 {x}^{2}\right) - \left(2 x - 3\right)$

$= 7 {x}^{2} \left(2 x - 3\right) - 1 \left(2 x - 3\right)$

$= \left(7 {x}^{2} - 1\right) \left(2 x - 3\right)$

$= \left({\left(\sqrt{7} x\right)}^{2} - {1}^{2}\right) \left(2 x - 3\right)$

$= \left(\sqrt{7} x - 1\right) \left(\sqrt{7} x + 1\right) \left(2 x - 3\right)$