# How do you factor 2x^3 + 2x^2 - 84x?

Aug 13, 2016

$2 x \left(x + 7\right) \left(x - 6\right)$

#### Explanation:

The first step is to take out the $\textcolor{b l u e}{\text{common factor}}$ of 2x

$\Rightarrow 2 x \left({x}^{2} + x - 42\right) \ldots \ldots . . \left(A\right)$

Now factorise the $\textcolor{b l u e}{\text{quadratic}}$ inside the bracket.

Using the a-c method, find the factors of - 42 which sum to +1

These are +7 and - 6

$\Rightarrow {x}^{2} + x - 42 = \left(x + 7\right) \left(x - 6\right)$

substituting these into (A) gives the factorised form.

$\Rightarrow 2 {x}^{3} + 2 {x}^{2} - 84 x = 2 x \left(x + 7\right) \left(x - 6\right)$

Aug 13, 2016

$2 x \left({x}^{2} + x - 42\right) = 2 x \left(x - 6\right) \left(x + 7\right)$
${x}^{2} + x - 42 = \left(x - 6\right) \left(x + 7\right)$ (If this were not immediately obvious, I could have used the quadratic equation and solved for $x$ in the quadratic.
And thus, $2 {x}^{3} + 2 {x}^{2} - 84 x$ $=$ $2 x \left(x - 6\right) \left(x + 7\right)$