How do you factor completely #2x^2+7x-15#?

1 Answer
Feb 10, 2017

Answer:

#2x^2+7x-15 = (2x-3)(x+5)#

Explanation:

Given:

#2x^2+7x-15#

Use an AC method:

Find a pair of factors of #AC=2*15=30# which differ by #B=7#.

The pair #10, 3# works.

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

#2x^2+7x-15 = (2x^2+10x)-(3x+15)#

#color(white)(2x^2+7x-15) = 2x(x+5)-3(x+5)#

#color(white)(2x^2+7x-15) = (2x-3)(x+5)#