Final answer:
To use the remainder theorem, substitute x = 2 into the function f(x) = x^3 - 8x, resulting in a remainder of -8 when divided by x - 2.
Step-by-step explanation:
To find the remainder when the function f(x) = x^3 - 8x is divided by x - 2 using the remainder theorem, we simply evaluate the function f at the value x = 2. The remainder theorem tells us that if a polynomial f(x) is divided by x - c, the remainder is f(c). So in this case:
f(2) = 2^3 - 8(2)
f(2) = 8 - 16
f(2) = -8
Therefore, the remainder is -8. The final answer in two line explanation in 300 words: By using the remainder theorem, we find that the remainder when f(x) is divided by x - 2 is f(2), which calculates to -8.