AnswersAZ-Common Core Algebra II AThe Rational Roots Theorem

The Rational Roots Theorem Answers

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

Question illustration
A
f(x) = 24x7 + 3x6 + 4x3 – x – 28
B
f(x) = 28x7 + 3x6 + 4x3 – x – 24
C
f(x) = 30x7 + 3x6 + 4x3 – x – 56
D
f(x) = 56x7 + 3x6 + 4x3 – x – 30
2
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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?

Question illustration
A
The root at point P may be .
Option A
B
The root at point P may be .
Option B
C
The root at point P may be .
Option C
D
The root at point P may be .
Option D
3

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

A
Any rational root of f(x) is a multiple of 12 divided by a multiple of 9.
B
Any rational root of f(x) is a multiple of 9 divided by a multiple of 12.
C
Any rational root of f(x) is a factor of 12 divided by a factor of 9.
D
Any rational root of f(x) is a factor of 9 divided by a factor of 12.
4

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)?

A
–4 and 3
B
–4, 2, and 3
C
–3 and 4
D
–3, 2, and 4
5

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

Question illustration
A
1
B
2
C
4
D
6
6

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

A
2x – 7
B
2x + 7
C
3x – 7
D
3x + 7
7

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

A
and
Option A
B
and
Option B
C
–1, , , and 1
Option C
D
–1, , , and 1
Option D
8

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

A
f(x) = (x + 2)(x – 3)(x + 6)
B
f(x) = (x + 2)(x – 3)(x – 6)
C
f(x) = (x – 2)(x + 3)(x – 1)
D
f(x) = (x + 2)(x – 3)(x – 1)
9

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

A
, , , , , 1, , 2, 4
Option A
B
, , , 1, , , 3, , 9
Option B
C
, , , , , 1, , 2, 4
Option C
D
, , , 1, , , 3, , 9
Option D
10

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)?

Question illustration
A
Negative six-fifths
Option A
B
Negative one-fourths
Option B
C
3
D
6

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