10
QuizMultiple Choice

The Rational Roots Theorem — Quiz

Question 10 • Mathematics III

According to the Rational Root Theorem, which statement about f of x is equal to 12 x cubed minus 5 x squared plus 6 x plus 9 is true?

Answer
A
Any rational root of f of x is a multiple of 9 divided by a multiple of 12 .
B
Any rational root of f of x is a multiple of 12 divided by a multiple of 9 .
C
Any rational root of f of x is a factor of 9 divided by a factor of 12 .
D
Any rational root of f of x is a factor of 12 divided by a factor of 9 .

Explanation

The Rational Root Theorem says any rational root of a polynomial written with integer coefficients must be a factor of the constant term divided by a factor of the leading coefficient. Here the constant term is 9 and the leading coefficient is 12, so any rational root must be a factor of 9 divided by a factor of 12. Therefore, the true statement is “Any rational root of f(x) is a factor of 9 divided by a factor of 12.”

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