# How do you factor completely #15a^2 + 55a - 20#?

##### 1 Answer

Oct 26, 2016

#### Explanation:

First separate out the common scalar factor

#15a^2+55a-20 = 5(3a^2+11a-4)#

Next use an AC Method to factor

Find a pair of factors of

The pair

Use this pair to split the middle term and factor by grouping:

#3a^2+11a-4 = 3a^2+12a-a-4#

#color(white)(3a^2+11a-4) = (3a^2+12a)-(a+4)#

#color(white)(3a^2+11a-4) = 3a(a+4)-1(a+4)#

#color(white)(3a^2+11a-4) = (3a-1)(a+4)#

So:

#15a^2+55a-20 = 5(3a-1)(a+4)#