Find the remainder when the polynomial (x^17 + 1) is divided by (x + 1).
x
x - 1
0
1
Correct answer: 0
Solution
By the Remainder Theorem, the remainder of f(x) divided by (x+1) equals f(-1). Here f(-1) = (-1)^17 + 1 = -1 + 1 = 0. So the remainder is 0, meaning (x+1) is a factor of (x^17+1).