# How do you factor x^3 - 2x^2 - 5x + 10?

Dec 20, 2015

Apply factoring by grouping to obtain

${x}^{3} - 2 {x}^{2} - 5 x + 10 = \left({x}^{2} - 5\right) \left(x - 2\right)$

#### Explanation:

${x}^{3} - 2 {x}^{2} - 5 x + 10 = {x}^{2} \left(x - 2\right) - 5 \left(x - 2\right)$

$= \left({x}^{2} - 5\right) \left(x - 2\right)$

We could further factor ${x}^{2} - 5 = \left(x + \sqrt{5}\right) \left(x - \sqrt{5}\right)$ by the difference of squares technique, however the above suffices if we only want a solution involving integers.