Question

H(x) = x - 1 is a factor of f(x) = x^5 + 1.
A) True
B) False

Answer 1

By substituting x = 1 into f(x) = x^5 + 1, we get f(1) = 2, which is not zero. Therefore, h(x) = x - 1 is not a factor of f(x), hence the statement is False.

Step-by-step explanation:

To determine whether h(x) = x - 1 is a factor of f(x) = x^5 + 1, we can use polynomial division or apply the Factor Theorem. According to the Factor Theorem, if x = a is a root of the polynomial f(x), then x - a is a factor of f(x). In other words, if we substitute a into f(x) and get zero, then x - a is a factor.

For h(x) = x - 1, the root would be x = 1. Substituting x=1 into f(x) gives us f(1) = 1^5 + 1 = 1 + 1 = 2. Since this does not equal zero, h(x) = x - 1 is not a factor of f(x) = x^5 + 1, making the statement False.