# How do you factor x^3+3x^2-x-3=0?

Dec 28, 2015

Alternatively, you can factor by grouping and using the difference of squares identity to find:

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

#### Explanation:

The difference of squares identity can be written:

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

Factor by grouping then using the difference of squares identity with $a = x$ and $b = 1$ as follows:

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

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

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

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

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

$= \left(x - 1\right) \left(x + 1\right) \left(x + 3\right)$