The Rational Roots Theorem

Question 1

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

Revolt · Accepted Answer

2

Question 2

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?

Revolt · Accepted Answer

f(x) = 3x5 – 2x4 – 9x3 + x2 – 12

Question 3

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

Revolt · Accepted Answer

and

Question 4

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 5

According to the Rational Root Theorem, the following are potential roots of f(x) = 60x2 – 57x – 18., , 3, 6Which is an actual root of f(x)?

Revolt · Accepted Answer

Negative one-fourths

Question 6

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 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

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 9

According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?

Revolt · Accepted Answer

Answer image: https://media.edgenuity.com/evresources/3111-06-04/mc004-2.jpg

Question 10

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.

The Rational Roots Theorem Answers