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:

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

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

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

How do you factor completely 2x^2+7x-152x^2+7x-15?