Answer:
To factor the expression 6x² + x - 12, we can use the following steps:
Look for a pair of factors of -12 whose sum is 1. The pairs of factors of -12 are (-1, 12), (2, -6), and (-3, 4). Since the coefficient of the x² term is 6, we want to choose (-3, 4) as our pair of factors.
Use the pair of factors (-3, 4) to write the expression as (6x² + (-3)x) + (4x - 12).
To complete the factoring, we need to find two binomial terms that add up to (6x² + (-3)x) and multiply to (4x - 12). The binomial terms that multiply to (4x - 12) are (2x - 3) and (3x - 4).
Therefore, the expression 6x² + x - 12 can be factored as (2x - 3)(3x - 4).
Therefore, the answer is D) (2x + 3)(3x - 4).