Find the remainder when f(x) is divided by (x - k); f(x) = 3x⁴ + 11x³ + 2x² - 7x + 61; k = 3.

Solution:

We will use the remainder theorem to find the remainder.

f(x) = 3x⁴ + 11x³ + 2x² - 7x + 61 is divided by (x - k)

⇒ x = k where value of k = 3 (given)

Substitute the value of x = k = 3 in the equation.

f(k = 3) = 3(3)⁴ + 11(3)³ + 2(3)² - 7(3) + 61

f(k) = 243 + 297 + 18 - 21 + 61

f(k) = 598

Find the remainder when f(x) is divided by (x - k); f(x) = 3x⁴ + 11x³ + 2x² - 7x + 61; k = 3.

Summary:

Therefore, the remainder when f(x) = 3x⁴ + 11x³ + 2x² - 7x + 61is divided by (x - k); k = 3 is 598.