AnswersFL-1200330-Algebra 2 CRSynthetic Division and the Remainder Theorem

The Rational Roots Theorem Answers

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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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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
3

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
4

The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below. How many roots of f(x) are rational numbers?

Question illustration
A
0
B
1
C
2
D
3
5

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.
6

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)
7

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
8

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

A
0
B
One-seventh
Option B
C
2
D
Seven-thirds
Option D
9

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.
10

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

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