Question

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

Answer 1

`(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)`

Answer 2

`(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)`.