# How do you factor -25x^2-70x+120?

May 30, 2015

First separate out the common factor $- 5$ ...

$- 25 {x}^{2} - 70 x + 120 = - 5 \left(5 {x}^{2} + 14 x - 24\right)$

Then, using a version of the AC Method, look for a pair of factors of $5 \cdot 24 = 120$, whose difference is $14$...

$20 \times 6 = 120$
$20 - 6 = 14$

Then use the pair we found to split the middle term and factor by grouping...

$- 5 \left(5 {x}^{2} + 14 x - 24\right)$

$= - 5 \left(5 {x}^{2} + 20 x - 6 x - 24\right)$

$= - 5 \left(\left(5 {x}^{2} + 20 x\right) - \left(6 x + 24\right)\right)$

$= - 5 \left(5 x \left(x + 4\right) - 6 \left(x + 4\right)\right)$

$= - 5 \left(5 x - 6\right) \left(x + 4\right)$