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The Rational Roots Theorem Answers

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What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?

and

and

–1, , , and 1

–1, , , and 1

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The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below. How many roots of f(x) are rational numbers?

What is the completely factored form of f(x) = x3 – 2x2 – 5x + 6?

f(x) = (x + 2)(x – 3)(x + 6)

f(x) = (x + 2)(x – 3)(x – 6)

f(x) = (x – 2)(x + 3)(x – 1)

f(x) = (x + 2)(x – 3)(x – 1)

Which is a factor of the polynomial f(x) = 6x4 – 21x3 – 4x2 + 24x – 35?

2x – 7

2x + 7

3x – 7

3x + 7

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

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

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

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

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

According to the Rational Root Theorem, is a potential rational root of which function?

f(x) = 24x7 + 3x6 + 4x3 – x – 28

f(x) = 28x7 + 3x6 + 4x3 – x – 24

f(x) = 30x7 + 3x6 + 4x3 – x – 56

f(x) = 56x7 + 3x6 + 4x3 – x – 30

The graph of f(x) = x6 – 2x4 – 5x2 + 6 is shown below. How many roots of f(x) are rational numbers?

According to the Rational Root Theorem, which statement about f(x) = 66x4 – 2x3 + 11x2 + 35 is true?

Any rational root of f(x) is a factor of 35 divided by a factor of 66.

Any rational root of f(x) is a multiple of 35 divided by a multiple of 66.

Any rational root of f(x) is a factor of 66 divided by a factor of 35.

Any rational root of f(x) is a multiple of 66 divided by a multiple of 35.

According to the Rational Root Theorem, which statement about f(x) = 12x3 – 5x2 + 6x + 9 is true?

Any rational root of f(x) is a multiple of 12 divided by a multiple of 9.

Any rational root of f(x) is a multiple of 9 divided by a multiple of 12.

Any rational root of f(x) is a factor of 12 divided by a factor of 9.

Any rational root of f(x) is a factor of 9 divided by a factor of 12.

According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 + 2x – 24.–4, –3, 2, 3, 4Which are actual roots of f(x)?

–4 and 3

–4, 2, and 3

–3 and 4

–3, 2, and 4

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The Rational Roots Theorem Answers

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