8
QuizMultiple Choice

The Rational Roots Theorem — Quiz

Question 8 • Mathematics III

According to the Rational Root Theorem, which statement about f of x is equal to 66 x to the 4th power minus 2 x cubed plus 11 x squared plus 35 is true?

Answer
A
Any rational root of f of x is a multiple of 35 divided by a multiple of 66 .
B
Any rational root of f of x is a multiple of 66 divided by a multiple of 35 .
C
Any rational root of f of x is a factor of 35 divided by a factor of 66 .
D
Any rational root of f of x is a factor of 66 divided by a factor of 35 .

Explanation

The Rational Root Theorem says a rational root in lowest terms, 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 35 and the leading coefficient is 66, so any rational root is a factor of 35 divided by a factor of 66.

AI-written and checked against the verified answer.

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