AnswersMathematics IIIOperating with Polynomials

Operating with Polynomials — Test Answers

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1
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What is the difference of the polynomials? open paren 12 x squared minus 11 y squared minus 13 x close paren minus open paren 5 x squared minus 14 y squared minus 9 x close paren

A
7 x squared minus 25 y squared minus 22 x
B
7 x squared minus 3 y squared minus 4 x
C
7 x squared plus 3 y squared minus 4 x
D
17 x squared minus 25 y squared minus 22 x
2
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Which polynomial is in standard form?

A
19 x plus 6 x squared plus 2
B
23 x to the 9th power minus 12 x to the 4th power plus 19
C
2 x to the 4th power plus 6 plus 24 x to the 5th power
D
6 x squared minus 9 x cubed plus 12 x to the 4th power
3

What is the product? 4 x times open paren negative 3 x to the 8th power close paren times open paren negative 7 x cubed close paren

A
negative 84 x to the 12th power
B
negative 84 x to the 24th power
C
84 x to the 24th power
D
84 x to the 12th power
6

Which expression is equivalent to open paren 3 x squared minus 7 close paren ?

A
open paren 10 x squared minus 4 close paren minus open paren 7 x squared plus 3 close paren
B
open paren 2 x squared minus 11 close paren minus open paren x squared plus 4 close paren
C
open paren 15 x squared plus 8 close paren minus open paren 18 x squared plus 1 close paren
D
open paren 5 x squared minus 6 close paren minus open paren 2 x squared minus 1 close paren
7

The missing term in the following polynomial has a degree of 5 and a coefficient of 16 square plus 13 x to the 6th power minus 11 x cubed minus 9 x squared plus 5 x minus 2 Which statement best describes the polynomial?

A
It is not in standard form because the degree of the first term is not greater than six.
B
It is not in standard form because the degree of the first term should be equal to zero.
C
It is in standard form because the coefficients are in order from highest to lowest.
D
It is in standard form because the exponents are in order from highest to lowest.
8

What is the difference of the polynomials? open paren m squared n squared minus 7 close paren minus open paren m n plus 4 close paren

A
m squared n squared minus m n minus 3
B
m n plus 3
C
m n minus 11
D
m squared n squared minus m n minus 11
9

Randy divides open paren 2 x to the 4th power minus 3 x cubed minus 3 x squared plus 7 x minus 3 close paren by open paren x squared minus 2 x plus 1 close paren as shown. What error does Randy make? Randy's Work Open image in full-screen view

A
He makes an error writing the constant term in the quotient.
B
He makes an error rewriting the problem in long division.
C
He makes a subtraction error.
D
He makes an error choosing the x -term in the quotient.
10

The volume of a rectangular prism is open paren x to the 4th power plus 4 x cubed plus 3 x squared plus 8 x plus 4 close paren , and the area of its base is open paren x cubed plus 3 x squared plus 8 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 plus 1 plus the fraction with numerator 4 and denominator x cubed plus 3 x squared plus 8
B
x plus 1 minus the fraction with numerator 4 and denominator x cubed plus 3 x squared plus 8
C
x plus 1 minus the fraction with numerator 4 and denominator x to the 4th power plus 4 x cubed plus 3 x squared plus 8 x plus 4
D
x plus 1 plus the fraction with numerator 4 and denominator x to the 4th power plus 4 x cubed plus 3 x squared plus 8 x plus 4
11

What is the completely factored form of p to the 4th power minus 16 ?

A
open paren p minus 2 close paren times open paren p minus 2 close paren times open paren p plus 2 close paren times open paren p plus 2 close paren
B
open paren p minus 2 close paren times open paren p minus 2 close paren times open paren p minus 2 close paren times open paren p minus 2 close paren
C
open paren p minus 2 close paren times open paren p plus 2 close paren times open paren p squared plus 4 close paren
D
open paren p minus 2 close paren times open paren p plus 2 close paren times open paren p squared plus 2 p plus 4 close paren
12

What is the completely factored form of x squared minus 16 x y plus 64 y squared ?

A
open paren x minus 8 y close paren times open paren x minus 8 y close paren
B
x y open paren x plus 16 plus 64 y close paren
C
x y open paren x minus 16 plus 64 y close paren
D
open paren x plus 8 y close paren times open paren x plus 8 y close paren
13

Vanessa uses the expressions open paren 3 x squared plus 5 x plus 10 close paren and open paren x squared minus 3 x minus 1 close paren to represent the length and width of her patio. Which expression represents the area l w of Vanessa’s patio?

A
3 x to the 4th power minus 4 x cubed plus 22 x squared plus 35 x plus 10
B
3 x to the 4th power plus 14 x cubed plus 28 x squared plus 35 x plus 10
C
3 x to the 4th power plus 14 x cubed plus 22 x squared plus 25 x minus 10
D
3 x to the 4th power minus 4 x cubed minus 8 x squared minus 35 x minus 10
15

A student factors 10 x squared plus 3 x minus 27 to the following. open paren 2 x minus 3 close paren times open paren 5 x plus 9 close paren Which statement about open paren 2 x minus 3 close paren times open paren 5 x plus 9 close paren is true?

A
The expression is not equivalent, but it is completely factored.
B
The expression is not equivalent, and it is not completely factored.
C
The expression is equivalent, but it is not completely factored.
D
The expression is equivalent, and it is completely factored.
18

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 minus the fraction with numerator 47 and denominator 3 x to the 4th power minus 4 x squared plus 8 x minus 1
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 x minus 2
D
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
19

What expression is equivalent to open paren 5 z squared plus 3 z plus 2 close paren squared ?

A
5 z to the 4th power plus 9 z squared plus 4
B
25 z to the 4th power plus 30 z cubed plus 29 z squared plus 12 z plus 4
C
5 z to the 4th power plus 3 z squared plus 4
D
25 z to the 4th power plus 30 z cubed plus 19 z squared plus 12 z plus 4
21

The volume of a cylinder is given by the formula cap v is equal to pi r squared h , where r is the radius of the cylinder and h is the height. Suppose a cylindrical can has radius open paren x plus 8 close paren and height open paren 2 x plus 3 close paren Which expression represents the volume of the can?

A
4 pi x cubed plus 44 pi x squared plus 105 pi x plus 72 pi
B
2 pi x cubed plus 35 pi x squared plus 80 pi x plus 48 pi
C
pi x cubed plus 19 pi x squared plus 112 pi x plus 192 pi
D
2 pi x cubed plus 35 pi x squared plus 176 pi x plus 192 pi

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