By applying the Remainder Theorem and substituting the value of k, we found that the remainder when dividing by (x - 6) is 0 and f(-3) is 144.
The correct answer is option D "144".
Finding the Value of f(-3)
Problem: When the polynomial f(x) = 3x² - 25x + k is divided by (x - 6), the remainder is 0. Find the value of f(-3).
Solution:
Remainder Theorem: If a polynomial function f(x) is divided by (x - a), the remainder is f(a). In this case, since the remainder when dividing by (x - 6) is 0, we know f(6) = 0.
Substitute f(6) = 0: Plug in x = 6 into the given function:
3 * 6² - 25 * 6 + k = 0
108 - 150 + k = 0
k = 42
Find f(-3): Now that we know k = 42, replace k in the original function:
f(-3) = 3 * (-3)² - 25 * (-3) + 42
27 + 75 + 42 = 144
Therefore, the value of f(-3) is 144.