The Rational Roots Theorem

Question 1

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

Revolt · Accepted Answer

f(x) = (x + 2)(x – 3)(x – 1)

Question 2

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15x11 – 6x8 + x3 – 4x + 3?

Revolt · Accepted Answer

, , , , , 3

Question 3

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

Revolt · Accepted Answer

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

Question 4

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

Revolt · Accepted Answer

f(x) = 24x7 + 3x6 + 4x3 – x – 28

Question 5

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

Revolt · Accepted Answer

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

Question 6

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

Revolt · Accepted Answer

3

Question 7

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)?

Revolt · Accepted Answer

–4 and 3

Question 8

The polynomial function f(x) = 10x6 + 7x – 7 is graphed below.According to the rational roots theorem, which is a possible root at point P?

Revolt · Accepted Answer

The root at point P may be .

Question 9

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

Revolt · Accepted Answer

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

Question 10

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9x4 – 2x2 – 3x + 4?

Revolt · Accepted Answer

, , , , , 1, , 2, 4

The Rational Roots Theorem Answers