The Rational Roots Theorem Answers

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

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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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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.
4

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
6

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
7

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)
8

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
9

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.

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