AnswersAlgebra IIThe Rational Roots Theorem

The Rational Roots Theorem — Quiz Answers

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1
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According to the Rational Roots Theorem, which statement about f of x is equal to 25 x to the 7th power minus x to the 6th power minus 5 x to the 4th power plus x minus 49 is true?

A
Any rational root of f of x is a multiple of negative 49 divided by a multiple of 25 .
B
Any rational root of f of x is a factor of negative 49 divided by a factor of 25 .
C
Any rational root of f of x is a factor of 25 divided by a factor of negative 49 .
D
Any rational root of f of x is a multiple of 25 divided by a multiple of negative 49 .
2
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According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g of x is equal to 3 x to the 5th power minus 2 x to the 4th power plus 9 x cubed minus x squared plus 12 ?

A
f of x is equal to 12 x to the 5th power minus 8 x to the 4th power plus 36 x cubed minus 4 x squared plus 48
B
f of x is equal to 3 x to the 5th power minus 2 x to the 4th power minus 9 x cubed plus x squared minus 12
C
f of x is equal to 12 x to the 5th power minus 2 x to the 4th power plus 9 x cubed minus x squared plus 3
D
f of x is equal to 3 x to the 6th power minus 2 x to the 5th power plus 9 x to the 4th power minus x cubed plus 12 x
3

According to the Rational Root Theorem, what are all the potential rational roots of f of x is equal to 9 x to the 4th power minus 2 x squared minus 3 x plus 4 ?

A
1 fourth , 1 half , 3 fourths , 1 , 3 halves , 9 fourths , 3 , 9 halves , 9
B
plus or minus 1 ninth , plus or minus 2 ninths , plus or minus 1 third , plus or minus 4 ninths , plus or minus 2 thirds , plus or minus 1 , plus or minus 4 thirds , plus or minus 2 , plus or minus 4
C
plus or minus 1 fourth , plus or minus 1 half , plus or minus 3 fourths , plus or minus 1 , plus or minus 3 halves , plus or minus 9 fourths , plus or minus 3 , plus or minus 9 halves , plus or minus 9
D
1 ninth , 2 ninths , 1 third , 4 ninths , 2 thirds , 1 , 4 thirds , 2 , 4
6

According to the Rational Root Theorem, negative 7 eighths is a potential rational root of which function?

A
f of x is equal to 28 x to the 7th power plus 3 x to the 6th power plus 4 x cubed minus x minus 24
B
f of x is equal to 56 x to the 7th power plus 3 x to the 6th power plus 4 x cubed minus x minus 30
C
f of x is equal to 30 x to the 7th power plus 3 x to the 6th power plus 4 x cubed minus x minus 56
D
f of x is equal to 24 x to the 7th power plus 3 x to the 6th power plus 4 x cubed minus x minus 28
8

According to the Rational Root Theorem, which statement about f of x is equal to 66 x to the 4th power minus 2 x cubed plus 11 x squared plus 35 is true?

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

According to the Rational Root Theorem, what are all the potential rational roots of f of x is equal to 15 x to the 11th power minus 6 x to the 8th power plus x cubed minus 4 x plus 3 ?

A
plus or minus 1 third , plus or minus 1 , plus or minus 5 thirds , plus or minus 3 , plus or minus 5 , plus or minus 15
B
plus or minus 1 third , plus or minus 1 , plus or minus 3
C
plus or minus 1 over 15 , plus or minus 1 fifth , plus or minus 1 third , plus or minus 3 fifths , plus or minus 1 , plus or minus 5 thirds , plus or minus 3 , plus or minus 5 , plus or minus 15
D
plus or minus 1 over 15 , plus or minus 1 fifth , plus or minus 1 third , plus or minus 3 fifths , plus or minus 1 , plus or minus 3
10

According to the Rational Root Theorem, which statement about f of x is equal to 12 x cubed minus 5 x squared plus 6 x plus 9 is true?

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

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