IXL - Rational root theorem (Precalculus practice)

A polynomial function

(

)

with integer coefficients has a leading coefficient of 9 and a constant term of 1. According to the Rational Root Theorem, which of the following are possible roots of

(

)

–

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Learn with an example

question

A polynomial function

(

)

with integer coefficients has a leading coefficient of

–

and a constant term of

–

According to the Rational Root Theorem, which of the following are possible roots of

(

)

–

key idea

(

)

is a polynomial and

is a number such that

(

)

then

is called a zero or root of

(

)

Rational Root Theorem

If a polynomial function

(

)

has integer coefficients and a non-zero constant term, then every rational root of

(

)

can be written in the form

, where:

a
is a factor of the constant term
b
is a factor of the leading coefficient

solution

According to the Rational Root Theorem, every rational root of

(

)

has a numerator that is a factor of the constant term,

–

and a denominator that is a factor of the leading coefficient,

–

Check which of the answer choices satisfy these conditions.

The number

is a possible root of

(

)

It has numerator 1, which is a factor of

–

and denominator 5, which is a factor of

–

The number

is a possible root of

(

)

It has numerator 1, which is a factor of

–

and denominator 1, which is a factor of

–

The number

–

is a possible root of

(

)

It has numerator

–

which is a factor of

–

and denominator 1, which is a factor of

–

The number

–

is a possible root of

(

)

It has numerator

–

which is a factor of

–

and denominator 5, which is a factor of

–

So, the answer choices that are possible roots of

(

)

are

–

and

–

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Not feeling ready yet? These can help:

E.1Prime factorization

F.1Find the roots of factored polynomials

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