The Rational Roots Theorem

Question 1

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 2

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 3

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 4

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 5

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

Revolt · Accepted Answer

and

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, 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 8

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 9

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 10

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

Revolt · Accepted Answer

2x – 7

The Rational Roots Theorem Answers