When x^3+2x+1 is divided by x+1, the remainder is −2. Apply the Remainder Theorem to find f(−1), where f(x)=x^3+2x+1.
The Remainder Theorem states that if a polynomial f(x) is divided by x - c, the remainder is equal to f(c). In this case, we are given that when f(x) = x^3 + 2x + 1 is divided by x + 1, the remainder is -2.
Therefore, f(-1) = -2.
To find f(-1) using the Remainder Theorem, we need to substitute -1 into the polynomial f(x) and find the value.
So, substituting x = -1 into f(x) = x^3 + 2x + 1:
f(-1) = (-1)^3 + 2(-1) + 1
= -1 - 2 + 1
= -2
Therefore, f(-1) = -2.