AnswersAZ-Common Core Algebra II AThe Rational Roots Theorem

The Rational Roots Theorem Answers

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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
2
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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.
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?

A
f(x) = 3x5 – 2x4 – 9x3 + x2 – 12
B
f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x
C
f(x) = 12x5 – 2x4 + 9x3 – x2 + 3
D
f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48
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)?

Question illustration
A
Negative six-fifths
Option A
B
Negative one-fourths
Option B
C
3
D
6
5

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
6

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

A
Any rational root of f(x) is a multiple of –49 divided by a multiple of 25.
B
Any rational root of f(x) is a multiple of 25 divided by a multiple of –49.
C
Any rational root of f(x) is a factor of –49 divided by a factor of 25.
D
Any rational root of f(x) is a factor of 25 divided by a factor of –49.
7

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

A
, , , , , 3
Option A
B
, , , , , , 3, 5, 15
Option B
C
, , 3
Option C
D
, , , 3, 5, 15
Option D
8

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

A
Any rational root of f(x) is a factor of 35 divided by a factor of 66.
B
Any rational root of f(x) is a multiple of 35 divided by a multiple of 66.
C
Any rational root of f(x) is a factor of 66 divided by a factor of 35.
D
Any rational root of f(x) is a multiple of 66 divided by a multiple of 35.
9

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
10

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

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