How do you factor the trinomial $x^2 + 3x - 40$ ?

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Answer 1 · 2016-05-03T21:49:22

$x^2+3x-40 = (x+8)(x-5)$

Note that:

$(x+a)(x-b) = x^2+(a-b)x-ab$

So we want to find $a, b > 0$ such that $a-b = 3$ and $ab=40$

The pair $8, 5$ works and hence:

$x^2+3x-40 = (x+8)(x-5)$

How do you factor the trinomial x^2 + 3x - 40x^2 + 3x - 40?