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

The Rational Roots Theorem Answers

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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.
2
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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
3

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
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, 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.
6

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.
7

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
8

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
9

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
10

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

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