Find the remainder when f(x) is divided by (x - k)
f(x) = 7x⁴ + 12x³ + 6x² - 5x + 16; k = 3

Solution:

We will use the remainder theorem to find the remainder.

f(x) = 7x⁴ + 12x³ + 6x² - 5x + 16 is divided by (x - k)

⇒ x = k where value of k = 3 (given)

Substitute the value of k = 3 for x.

f(k = 3) = 7(3)⁴ + 12(3)³ + 6(3)² - 5(3) + 16

f(k = 3) = 567 + 324 + 54 - 15 + 16

f(k = 3) = 567 + 324 + 54 + 1

f(k = 3)= 946

Find the remainder when f(x) is divided by (x - k)
f(x) = 7x⁴ + 12x³ + 6x² - 5x + 16; k = 3

Summary: 

The remainder when f(x) = 7x⁴ + 12x³ + 6x² - 5x + 16 is divided by (x - k); k = 3 is 946.