# How do you factor 15x^2 - x – 2 by grouping?

Jun 16, 2016

$15 {x}^{2} - x - 2 = \left(3 x + 1\right) \left(5 x - 2\right)$

#### Explanation:

To factorize $15 {x}^{2} - x - 2$ by grouping, we have to first split coefficient of middle term $- 1$ in two parts so that their product is the product of coefficient of other two i.e. $15 \times \left(- 2\right) = - 30$.

It is apparent that these could be $- 6$ and $5$. Hence,

$15 {x}^{2} - x - 2$

= $15 {x}^{2} - 6 x + 5 x - 2$

Now we group them as follows

$3 x \left(5 x - 2\right) + 1 \left(5 x - 2\right)$

= $\left(3 x + 1\right) \left(5 x - 2\right)$