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Polynomial Operations — Test Answers

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The quotient of open paren x to the 5th power minus 3 x cubed minus 3 x squared minus 10 x plus 15 close paren and open paren x squared minus 5 close paren is a polynomial. What is the quotient?

A
x to the 7th power minus 8 x to the 5th power minus 3 x to the 4th power plus 5 x cubed plus 30 x squared plus 50 x minus 75
B
x cubed plus 2 x minus 3
C
x to the 5th power minus 3 x cubed minus 4 x squared minus 10 x plus 20
D
x to the 5th power minus 3 x cubed minus 2 x squared minus 10 x plus 10
3

The volume of a rectangular prism is open paren x cubed minus 3 x squared plus 5 x minus 3 close paren , and the area of its base is open paren x squared minus 2 close paren If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

A
x minus 3 plus the fraction with numerator 7 x minus 9 and denominator x cubed minus 3 x squared plus 5 x minus 3
B
x minus 3 plus the fraction with numerator 7 x plus 3 and denominator x squared minus 2
C
x minus 3 plus the fraction with numerator 7 x minus 9 and denominator x squared minus 2
D
x minus 3 plus the fraction with numerator 7 x plus 3 and denominator x cubed minus 3 x squared plus 5 x minus 3
4

What is the quotient of open paren 3 x to the 4th power minus 4 x squared plus 8 x minus 1 close paren divided by open paren x minus 2 close paren ?

A
3 x cubed plus 6 x squared plus 8 x plus 24 plus the fraction with numerator 47 and denominator x minus 2
B
3 x cubed plus 6 x squared plus 8 x plus 24 minus the fraction with numerator 47 and denominator x minus 2
C
3 x cubed plus 6 x squared plus 8 x plus 24 plus the fraction with numerator 47 and denominator 3 x to the 4th power minus 4 x squared plus 8 x minus 1
D
3 x cubed plus 6 x squared plus 8 x plus 24 minus the fraction with numerator 47 and denominator 3 x to the 4th power minus 4 x squared plus 8 x minus 1
5

Which expression is equivalent to the fraction with numerator 60 x to the 20th power y to the 24th power and denominator 30 x to the 10th power y to the 12th power ?

A
30 x to the 10th power y to the 12th power
B
2 x squared y squared
C
30 x squared y squared
D
2 x to the 10th power y to the 12th power
6

Anja divides open paren 8 x cubed minus 36 x squared plus 54 x minus 27 close paren by open paren 2 x minus 3 close paren as shown. What error does Anja make? Anja's Work Expand Image

A
She makes an error rewriting the problem in long division.
B
She makes a multiplication error.
C
She makes an error choosing the x -term in the quotient.
D
She makes a subtraction error.
7

Which expression is equivalent to 5 r to the 6th power t to the 4th power open paren the fraction with numerator 4 r cubed s squared t to the 4th power and denominator 2 r to the 4th power st to the 6th power close paren to the 5th power ?

A
the fraction with numerator 160 r s to the 5th power and denominator t to the 6th power
B
the fraction with numerator 50 r s to the 5th power and denominator t to the 6th power
C
the fraction with numerator 160 s to the 6th power and denominator t cubed
D
the fraction with numerator 50 s to the 6th power and denominator t cubed
9

Which values of A and b make the equation true? the fraction with numerator open paren 2 x y close paren to the 4th power and denominator 4 x y is equal to 4 x to the A th power y to the b th power

A
A is equal to 4 , b is equal to 4
B
A is equal to 5 , b is equal to 5
C
A is equal to 3 , b is equal to 3
D
A is equal to 0 , b is equal to 0
10

The quotient of open paren x to the 4th power plus 5 x cubed minus 3 x minus 15 close paren and open paren x cubed minus 3 close paren is a polynomial. What is the quotient?

A
x minus 5
B
x plus 5
C
x to the 7th power plus 5 x to the 6th power plus 6 x to the 4th power plus 30 x cubed plus 9 x plus 45
D
x to the 7th power plus 5 x to the 6th power minus 6 x to the 4th power minus 30 x cubed plus 9 x plus 45
13

Which expression is equivalent to open paren the fraction with numerator m to the 5th power n and denominator p q squared close paren to the 4th power ?

A
the fraction with numerator m to the 9th power n to the 5th power and denominator p to the 5th power q to the 6th power
B
the fraction with numerator m to the 20th power n to the 4th power and denominator p to the 4th power q to the 8th power
C
the fraction with numerator m to the 9th power n to the 4th power and denominator p to the 4th power q to the 6th power
D
the fraction with numerator m to the 20th power n to the 4th power and denominator p q squared
15

What is the product? open paren y squared plus 3 y plus 7 close paren times open paren 8 y squared plus y plus 1 close paren

A
8 y to the 4th power plus 25 y cubed plus 60 y squared plus 10 y plus 7
B
8 y to the 4th power plus 25 y cubed plus 4 y squared plus 10 y plus 7
C
8 y to the 4th power plus 24 y cubed plus 60 y squared plus 10 y plus 7
D
8 y to the 4th power plus 25 y cubed plus 60 y squared plus 7 y plus 7
16

What is the product? open paren negative 6 A cubed b plus 2 A b squared close paren times open paren 5 A squared minus 2 A b squared minus b close paren

A
30 A to the 6th power b minus 12 A cubed b squared minus 6 A cubed b plus 10 A squared b squared minus 4 A b to the 4th power minus 2 A b squared
B
negative 30 A to the 5th power b plus 12 A to the 4th power b cubed plus 16 A cubed b squared minus 4 A squared b to the 4th power minus 2 A b cubed
C
30 A to the 5th power b minus 12 A to the 4th power b cubed plus 4 A cubed b squared minus 4 A squared b to the 4th power minus 2 A b cubed
D
negative 30 A to the 6th power b plus 12 A cubed b squared plus 6 A cubed b plus 10 A squared b squared minus 4 A b to the 4th power minus 2 A b squared
17

Which expression is equivalent to 16 cubed ?

A
2 to the 12th power
B
2 to the 64th power
C
2 to the 7th power
D
2 to the 11th power
18

Which expression is equivalent to the fraction with numerator open paren 4 g cubed h squared k to the 4th power close paren cubed and denominator 8 g cubed h squared minus open paren 5th power of h k cubed close paren to the 5th power ?

A
8 6th power of g 4th power of h k to the 12th power minus 25th power of h k to the 15th power
B
8 g cubed h cubed k to the 12th power minus 25th power of h k to the 15th power
C
8 9th power of g 7th power of h k to the 7th power minus 10th power of h k to the 8th power
D
8 g squared h cubed k to the 7th power minus 10th power of h k to the 8th power

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