Question

factoring trinomials with leading coefficient -6x to the power of 2 + x +12

Answer 1

Factor -6x^2 + x + 12.

1. Factor out -1:
-6x^2 + x + 12 = -(6x^2 - x - 12)

2. Use the ac-method on 6x^2 - x - 12:
a*c = 6 * (-12) = -72. Find two integers that multiply to -72 and add to -1: -9 and 8.

3. Split the middle term and group:
6x^2 + 8x - 9x - 12 = (6x^2 + 8x) + (-9x - 12)
= 2x(3x + 4) - 3(3x + 4)
= (3x + 4)(2x - 3)

4. Include the removed -1:
-6x^2 + x + 12 = -(3x + 4)(2x - 3)

You can also write the result as (3 - 2x)(3x + 4).