How do you factor a^2+a-12a2+a12?

2 Answers
Jun 25, 2018

(a-3)(a+4)(a3)(a+4)

Explanation:

Solving the quadratic equation by the quadratic Formula we get

a_(1,2)=-1/2pmsqrt(1/4+48/4)a1,2=12±14+484
a_(1,2)=-1/2pm7/2a1,2=12±72

we get

a_1=3a1=3

a_2=-4a2=4

so our factorization is given by

(a-3)(a+4)(a3)(a+4)

Jun 25, 2018

(a+4)(a-3)(a+4)(a3)

Explanation:

If we factor it into linear brackets (a-b)(a-c)(ab)(ac), then a^2+a-12=a^2-(b+c)a+bca2+a12=a2(b+c)a+bc. So bc=-12bc=12 and -(b+c)=1(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)a2+a12=(a+4)(a3).