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

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

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