AnswersAlgebra 1Polynomial Expressions

Polynomial Expressions — Test Answers

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Which algebraic expression is a polynomial with a degree of 2 ?

A
10 x squared minus square root of x
B
4 x cubed minus 2 x
C
6 x squared minus 6 x plus 5
D
8 x cubed plus 5 over x plus 3
2
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How could Brent use a rectangle to model the factors of x squared minus 7 x plus 6 ?

A
He could draw a diagram of a rectangle with dimensions x minus 4 and x plus 3 and then show the area is equivalent to the sum of x squared , negative 4 x , 3 x , and half of negative 12 .
B
He could draw a diagram of a rectangle with dimensions x minus 1 and x minus 6 and then show the area is equivalent to the sum of x squared , negative x , negative 6 x , and 6 .
C
He could draw a diagram of a rectangle with dimensions x minus 3 and x minus 4 and then show the area is equivalent to the sum of x squared , negative 3 x , negative 4 x , and half of 12 .
D
He could draw a diagram of a rectangle with dimensions x plus 7 and x minus 1 and then show the area is equivalent to the sum of x squared , 7 x , negative x , and 6 .
3

The expression 40 x squared minus 65 x plus 50 represents the sum of the interior angles of a regular pentagon in degrees. If the interior angles of the pentagon are equal, which expression represents the measure of two angles?

A
2 x squared open paren 20 minus 32 x plus 25 x squared close paren
B
2 times open paren 8 x squared minus 13 x plus 10 close paren
C
5 x squared open paren 8 x squared minus 13 x plus 10 close paren
D
5 times open paren 3 x squared minus 8 x plus 5 close paren
4

A square has a perimeter of 12 x plus 52 units. Which expression represents the side length of the square in units?

A
x plus 40
B
3 x plus 43
C
x plus 4
D
3 x plus 13
5

The expression y squared minus 10 y plus 24 has a factor of open paren y minus 4 close paren What is another factor of y squared minus 10 y plus 24 ?

A
open paren y minus 6 close paren
B
open paren y minus 14 close paren
C
open paren y minus 8 close paren
D
open paren y minus 20 close paren
6

What is the quotient? x minus 1 longdiv 7 x squared minus 3 x minus 9

A
7 x plus 4 minus the fraction with numerator 13 and denominator x minus 1
B
7 x minus 10 minus the fraction with numerator 19 and denominator x minus 1
C
7 x plus 4 minus the fraction with numerator 5 and denominator x minus 1
D
7 x minus 10 plus the fraction with numerator 1 and denominator x minus 1
7

Which shows one way to determine the factors of 4 x cubed plus x squared minus 8 x minus 2 by grouping?

A
x squared times open paren 4 x minus 1 close paren plus 2 times open paren 4 x minus 1 close paren
B
4 x squared open paren x minus 2 close paren minus 1 times open paren x minus 2 close paren
C
x squared times open paren 4 x plus 1 close paren minus 2 times open paren 4 x plus 1 close paren
D
4 x squared open paren x plus 2 close paren minus 1 times open paren x plus 2 close paren
8

What is the difference of the polynomials? open paren 8 r to the 6th power s cubed minus 9 r to the 5th power s to the 4th power plus 3 r to the 4th power s to the 5th power close paren minus open paren 2 r to the 4th power s to the 5th power minus 5 r cubed s to the 6th power minus 4 r to the 5th power s to the 4th power close paren

A
8 r to the 6th power s cubed minus 5 r to the 5th power s to the 4th power plus r to the 4th power s to the 5th power plus 5 r cubed s to the 6th power
B
8 r to the 6th power s cubed minus 13 r to the 5th power s to the 4th power plus r to the 4th power s to the 5th power minus 5 r cubed s to the 6th power
C
6 r to the 6th power s cubed minus 4 r to the 5th power s to the 4th power plus 7 r to the 4th power s to the 5th power
D
6 r to the 6th power s cubed minus 13 r to the 5th power s to the 4th power minus r to the 4th power s to the 5th power
9

Factor negative 7 x cubed plus 21 x squared plus 3 x minus 9 by grouping. What is the resulting expression?

A
open paren 7 x minus 3 close paren times open paren 3 plus x squared close paren
B
open paren 7 x squared minus 3 close paren times open paren 3 plus x close paren
C
open paren 3 minus 7 x squared close paren times open paren x minus 3 close paren
D
open paren 3 minus 7 x close paren times open paren x squared minus 3 close paren
10

The revenue, in dollars, of a company that produces jeans can be modeled by 2 x squared plus 17 x minus 175 The cost, in dollars, of producing the jeans can be modeled by 2 x squared minus 3 x minus 125 The number of pairs of jeans that have been sold is represented by x If the profit is the difference between the revenue and the cost, which expression can be used to find the profit and what is that profit when 75 pairs of jeans are sold?

A
20 x minus 50 ; 500 dollars
B
20 x minus 50 ; 1 dollars comma 450
C
20 x plus 50 ; 1 dollars comma 550
D
20 x plus 50 ; 5 dollars comma 250
11

What is the product of open paren 2 p plus 7 close paren times open paren 3 p squared plus 4 p minus 3 close paren ?

A
6 p cubed plus 29 p squared minus 22 p plus 21
B
6 p cubed plus 29 p squared plus 22 p minus 21
C
6 p cubed plus 29 p squared plus 34 p minus 21
D
6 p cubed plus 29 p squared minus 34 p plus 21
12

What is the greatest common factor of 8 x and 40 y ?

A
320
B
8
C
8 x y
D
320 x y
13

Simplify the expression negative 2 times open paren p plus 4 close paren squared minus 3 plus 5 p What is the simplified expression in standard form?

A
4 p squared plus 37 p minus 67
B
2 p squared plus 21 p plus 29
C
negative 2 p squared minus 11 p minus 35
D
negative 2 p squared plus 13 p plus 13
14

The first step when dividing 9⁢m2−4⁢m−6 by 3⁢m is shown. the fraction with numerator 9 m squared and denominator 3 m minus 4 m over 3 m minus 6 over 3 m Which could be the next step?

A
3 m minus 4 thirds minus m over 2
B
3 m minus 3 fourths minus 2 over m
C
3 m minus 4 thirds minus 2 over m
D
3 m minus 3 fourths minus m over 2
15

Factor x cubed minus 7 x raised to the 2 power minus 5 x plus 35 by grouping. What is the resulting expression?

A
open paren x squared minus 5 close paren times open paren x minus 7 close paren
B
open paren x squared minus 7 close paren times open paren x plus 5 close paren
C
open paren x squared minus 7 close paren times open paren x minus 5 close paren
D
open paren x squared plus 5 close paren times open paren x minus 7 close paren
16

What is the quotient? x plus 1 longdiv 3 x squared minus 2 x plus 7

A
3 x minus 5 plus the fraction with numerator 2 and denominator x plus 1
B
3 x plus 5 plus the fraction with numerator 12 and denominator x plus 1
C
3 x plus 5 plus the fraction with numerator 2 and denominator x plus 1
D
3 x minus 5 plus the fraction with numerator 12 and denominator x plus 1
17

Which is true about the polynomial negative 3 x y squared plus 5 x squared y ?

A
It is a binomial with a degree of 3 .
B
It is a trinomial with a degree of 2 .
C
It is a binomial with a degree of 2 .
D
It is a trinomial with a degree of 3 .
18

What is the sum of the polynomials? open paren 7 x cubed minus 4 x squared close paren plus open paren 2 x cubed minus 4 x squared close paren

A
9 x cubed minus 8 x squared
B
5 x cubed
C
9 x cubed
D
5 x cubed minus 8 x squared
19

What is the factored form of the polynomial? x squared minus 16 x plus 48

A
open paren x plus 4 close paren times open paren x plus 12 close paren
B
open paren x minus 6 close paren times open paren x minus 8 close paren
C
open paren x minus 4 close paren times open paren x minus 12 close paren
D
open paren x plus 6 close paren times open paren x plus 8 close paren
20

Which terms could have a greatest common factor of 5 m squared n squared ? Choose two correct answers.

A
10 m to the 4th power n
B
5 m to the 4th power n cubed
C
m to the 5th power n to the 5th power
D
24 m cubed n to the 4th power
E
15 m squared n squared

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