Factor the given polynomial.

3x² + 5x - 12

= (x + 3) (3 x - 4)

Step-by-step explanation:

Use a version of the AC Method.

A = 3, B = 5, C = 12

Since the sign on the constant term is -, look for a pair of factors of A C = 36 whose difference is B = 5

The pair 4, 9 works.

Now use that pair to split the middle term, then factor by grouping:

3 x 2 + 5 x - 12 = 3 x

- 4 x + 9 x - 12 = (3 x 2 - 4 x) + (9 x - 12) = x (3 x - 4) + 3 (3 x - 4)