How do you factor the trinomial $x^2+x-12$ ?

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Answer 1 · 2017-01-17T18:49:56

$x^2+x-12 = (x+4)(x-3)$

Note that:

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

So if we can find two positive numbers $a, b$ such that $a-b=1$ and $ab = 12$ then we have a factorisation.

The numbers $a=4$ and $b=3$ work, so we find:

$x^2+x-12 = (x+4)(x-3)$

How do you factor the trinomial x^2+x-12x^2+x-12?