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

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Answer 1 · 2017-02-10T00:11:52

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

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)#