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Factor 6x² + x - 12 into two binomial terms.

A) (2x - 4)(3x + 3)
B) x(6x + 1) - 12
C) (3x + 4)(2x - 3)
D) (2x + 3)(3x - 4)

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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).

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