# How do you factor 10x^2 - 8x - 15x + 12?

May 16, 2018

$\left(2 x - 3\right) \left(5 x - 4\right)$

#### Explanation:

$\text{if the ratios of the coefficients of the first/second terms}$
$\text{and third/fourth terms are equal we can factor by grouping}$

$\text{As they stand this is not the case but rearranging gives}$

$10 {x}^{2} - 15 x - 8 x + 12 \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

$= \textcolor{red}{5 x} \left(2 x - 3\right) \textcolor{red}{- 4} \left(2 x - 3\right)$

$\text{take out the "color(blue)"common factor } \left(2 x - 3\right)$

$= \left(2 x - 3\right) \left(\textcolor{red}{5 x - 4}\right)$

$\Rightarrow 10 {x}^{2} - 8 x - 15 x + 12 = \left(2 x - 3\right) \left(5 x - 4\right)$