Synthetic Division and the Remainder Theorem — Unit test

Question 1 • FL-1200330-Algebra 2 CR

If (x – 5) is a factor of f(x), which of the following must be true?

Answer

A root of f(x) is x = –5.

A root of f(x) is x = 5.

Both x = –5 and x = 5 are roots of f(x).

Neither x = –5 nor x = 5 is a root of f(x).

Explanation

By the factor theorem, if (x − 5) is a factor of f(x), then f(5) = 0. That means x = 5 is a root of f(x). The factor does not imply that x = −5 is also a root, so the correct choice is “A root of f(x) is x = 5.”

AI-written and checked against the verified answer.

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