How do you factor a^2+a-12?

2 Answers
Jun 25, 2018

(a-3)(a+4)

Explanation:

Solving the quadratic equation by the quadratic Formula we get

a_(1,2)=-1/2pmsqrt(1/4+48/4)
a_(1,2)=-1/2pm7/2

we get

a_1=3

a_2=-4

so our factorization is given by

(a-3)(a+4)

Jun 25, 2018

(a+4)(a-3)

Explanation:

If we factor it into linear brackets (a-b)(a-c), then a^2+a-12=a^2-(b+c)a+bc. So bc=-12 and -(b+c)=1. So we're looking for values that are of opposite sign, multiply to -12, and whose absolute values are 1 apart. 4 and 3 is where we are looking, and specifically, -4 and +3 are the answers, which we find by a small amount of trial and error.

So a^2+a-12=(a+4)(a-3).