Question

Factor this polynomial completely. 12x^2+ x-6

Answer 1

Answer:

(3 x - 2) (4 x + 3)

Step-by-step explanation:

Factor the following:

12 x^2 + x - 6

Factor the quadratic 12 x^2 + x - 6.

The coefficient of x^2 is 12 and the constant term is -6.

The product of 12 and -6 is -72. The factors of -72 which sum to 1 are -8 and 9.

So 12 x^2 + x - 6 = 12 x^2 + 9 x - 8 x - 6 = 3 (3 x - 2) + 4 x (3 x - 2):

3 (3 x - 2) + 4 x (3 x - 2)

Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2):

Answer:  (3 x - 2) (4 x + 3)