Question

Find the remainder when f(x) is divided by (x - k)

f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3

Answer 1

Answer: The remainder is 946.

Explanation:

Answer 2

By the remainder theorem, the remainder when (x - k) divides f(x) is f(k).
f(x) = 7x^4 + 12x^3 + 6x^2 - 5x + 16
f(3) = 7(3)^4 + 12(3)^3 + 6(3)^2 - 5(3) + 16 = 7(81) + 12(27) + 6(9) - 15 + 16 = 567 + 324 + 54 + 1 = 946
Therefore, remainder is 946