Final answer:
To find the value of k, substitute -3 into the equation and equate it to the remainder. Then solve for k.
Step-by-step explanation:
To find the value of k, we need to determine the remainder when f(x) is divided by (x + 3). The remainder can be found by substituting -3 into the equation f(x) and equating it to 52.
So, f(-3) = 2(-3)² - 5(-3) + k = 9 + 15 + k = 24 + k.
Since the remainder is 52, we have: 24 + k = 52. Solving for k, we get k = 52 - 24 = 28.
Learn more about Dividing polynomials