8
QuizMultiple Choice

The Rational Roots Theorem

Question 8 • AZ-Common Core Algebra II A

According to the Rational Roots Theorem, which statement about f(x) = 25x7 – x6 – 5x4 + x – 49 is true?

Answer
A
Any rational root of f(x) is a multiple of –49 divided by a multiple of 25.
A
Any rational root of f(x) is a multiple of 25 divided by a multiple of –49.
A
Any rational root of f(x) is a factor of –49 divided by a factor of 25.
A
Any rational root of f(x) is a factor of 25 divided by a factor of –49.

Explanation

The Rational Roots Theorem says a rational root, written in lowest terms as p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient. Here the constant term is −49 and the leading coefficient is 25, so any rational root must be a factor of −49 divided by a factor of 25. That is choice C.

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