Question

(03.01r)
given a polynomial f(x), if (x - 1) is a factor, what else must be true?
f(0) = 1
f(1) = 0
f(-1) = 0
f(0) = -1

Explanation:

Step1: Recall the Factor Theorem

The Factor Theorem states that if \((x - a)\) is a factor of a polynomial \(f(x)\), then \(f(a)=0\).

Step2: Apply the Factor Theorem to the given factor

Here, the factor is \((x - 1)\), so \(a = 1\). By the Factor Theorem, we must have \(f(1)=0\).

Answer:

\(f(1) = 0\) (corresponding to the option with \(f(1)=0\))