The Rational Roots Theorem

Question 1

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

Revolt · Accepted Answer

2x – 7

Question 2

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

Revolt · Accepted Answer

and

Question 3

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

Question 4

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 5

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 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 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 8

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 9

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

Revolt · Accepted Answer

f(x) = (x + 2)(x – 3)(x – 1)

The Rational Roots Theorem Answers