Final answer:
To find the quotient of (15x^2 - 8x - 12) and (3x + 2), use long division. The quotient is 5x - 6.
Step-by-step explanation:
To find the quotient of (15x^2 - 8x - 12) and (3x + 2), we need to divide the polynomial (15x^2 - 8x - 12) by the binomial (3x + 2).
We can use long division to do this. Start by dividing the first term, 15x^2, by the first term of the binomial, 3x, which gives us 5x.
Next, multiply the binomial by 5x, which gives us 15x^2 + 10x.
Subtract this result from the original polynomial to get -18x - 12. Now, continue the long division process with -18x - 12 and (3x + 2).
Continuing the long division, divide -18x by 3x to get -6 and multiply the binomial by -6, which gives -18x - 12.
Subtract this result from the remainder, -6, to get 0. Since the remainder is 0, we have found the quotient.
Therefore, the quotient of (15x^2 - 8x - 12) and (3x + 2) is 5x - 6.