Question

Given f(x) = x^3 + kx - 15 and the remainder when f(x) is divided by x - 3 is -18, what is the value of k?

A) k = 0
B) k = -3
C) k = 6
D) k = -6

Answer 1

Using the Remainder Theorem, we substitute x with 3 in the function's formula and then solve for k, but the result does not match any of the provided choices. There might be an error in the problem or the answer choices.

Step-by-step explanation:

The student is asking about finding the value of k in a polynomial function when given a specific remainder from division by a binomial. In this case, the function f(x) = x^3 + kx - 15 is divided by x - 3, and the remainder is -18. To find k, we can use the Remainder Theorem, which states that the remainder of the division of a polynomial f(x) by x - a is f(a). Substituting x with 3 in the function and equating it to -18, we get:

3^3 + 3k - 15 = -18

This simplifies to:

27 + 3k - 15 = -18

Adding 15 to both sides and then subtracting 27 we get:

3k = -18 - 15 + 27

3k = -6

Dividing by 3:

k = -2

However, none of the given choices matches k = -2, which indicates a possible mistake in the problem or the answer choices. Normally, we would solve for k and match it with the given choices. In this case, there may be an error in the assessment of the problem.