Final answer:
The remainder when dividing the polynomial x³-2x²+x-4 by x-2, found using the Remainder Theorem, is -2.
Step-by-step explanation:
The question asks for the remainder when the polynomial x³-2x²+x-4 is divided by x-2. To find the remainder, we can use synthetic division or the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x - a, the remainder is f(a). So to find the remainder of our polynomial divided by x-2, we simply need to evaluate it at x=2.
Evaluating the polynomial f(x) = x³-2x²+x-4 at x=2 gives us f(2) = 2³ - 2(2²) + 2 - 4 = 8 - 8 + 2 - 4 = -2. Therefore, the remainder is -2.