The Polynomial Remainder Theorem states that if you divide a polynomial f(x) by (x - a), the remainder is equal to f(a). In this case, you want to evaluate the polynomial f(x) = x^3 - 3x^2 + 4x - 2 at x = 5.
f(5) = 5^3 - 3(5)^2 + 4(5) - 2
Now, calculate the values:
f(5) = 125 - 3(25) + 20 - 2
f(5) = 125 - 75 + 20 - 2
f(5) = 125 - 75 - 2 + 20
f(5) = 50 - 2 + 20
f(5) = 48 + 20
f(5) = 68
So, when you evaluate the polynomial f(x) at x = 5, you get f(5) = 68.