Final answer:
To find the remainder when the polynomial f(x) is divided by (x - k) with x = 2, we use the Remainder Theorem and evaluate f(2), resulting in a remainder of 37.
Step-by-step explanation:
The question asks to find the remainder when a polynomial f(x) is divided by (x - k). The polynomial given is f(x) = 4x³ - 6x² + 8x + 13, and we are asked to find the remainder for x = 2. To do this, we use the Remainder Theorem which states that the remainder of the division of a polynomial f(x) by a linear binomial (x - k) is equal to f(k).
By plugging in x = 2 into the polynomial, we get:
f(2) = 4(2)³ - 6(2)² + 8(2) + 13
<= 4(8) - 6(4) + 16 + 13
<= 32 - 24 + 16 + 13
<= 37
Therefore, the remainder when f(x) is divided by (x - 2) is 37.