# How do you factor a^3 - 2a^2 - 4a = -8?

Feb 11, 2016

You must mean to ask how to solve the equation.

#### Explanation:

Put everything to one side of the equation:

${a}^{3} - 2 {a}^{2} - 4 a + 8 = 0$

Factor out a common factor from two groups: the first 2 terms and last 2 terms.

${a}^{2} \left(a - 2\right) - 4 \left(a - 2\right) = 0$

$\left({a}^{2} - 4\right) \left(a - 2\right) = 0$

$\left(a + 2\right) \left(a - 2\right) \left(a - 2\right) = 0$

$a = - 2 \mathmr{and} 2$

The polynomial is completely factored and the solution set is $a = \pm 2$.

Hopefully this helps.