Final answer:
The value of k is obtained by factoring the quadratic expression 2x^2 + 5x - 12, where k corresponds to the number that satisfies the rewriting in the form (2x-3)(x+k). After factoring, k is found to be 4.
Step-by-step explanation:
If the given expression 2x^2 + 5x - 12 is rewritten in the form (2x-3)(x+k), where k is a constant, what is the value of k? To find the value of k, we need to factor the quadratic expression. We look for two numbers that multiply to (2 * -12) = -24 and add to the middle coefficient, which is 5. Those numbers are 8 and -3, because 8 * -3 = -24 and 8 - 3 = 5. By rewriting the expression as (2x^2 + 8x) + (-3x - 12) and grouping, we can rewrite the expression as 2x(x+4) - 3(x+4), which further simplifies to (2x - 3)(x + 4). Here, we see that the value of k is 4.