Question 1

Multiply.
-$( x - 5 ) ( 5 x - 4 )$

Accepted Answer

A)  $5 x ^ { 2 } - 31 x + 20$ 
B)  $5 x ^ { 2 } - 29 x + 20$ 
C)  $5 x ^ { 2 } + 20 x - 29$ 
D)  $5 x ^ { 2 } - 29 x - 29$ 
A)  $5 x ^ { 2 } - 31 x + 20$ 
B)  $5 x ^ { 2 } - 29 x + 20$ 
C)  $5 x ^ { 2 } + 20 x - 29$ 
D)  $5 x ^ { 2 } - 29 x - 29$

Question 2

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
-$$13 x ^ { 4 } + 7 x ^ { 3 } - 6 x - 3 y ^ { 5 }$$

Accepted Answer

A)  trinomial of degree 4 
B)  degree 5 ; none of these 
C)  degree 4 ; none of these 
D)  trinomial of degree 5 
A)  trinomial of degree 4 
B)  degree 5 ; none of these 
C)  degree 4 ; none of these 
D)  trinomial of degree 5

Question 3

Solve.
-The sum of two numbers is 17, and the sum of their squares is 145. Find the numbers.

Accepted Answer

A)  8 and 9 
B)  -8 and 9 
C)  -8 and -9 
D)  17 and 0 
A)  8 and 9 
B)  -8 and 9 
C)  -8 and -9 
D)  17 and 0

Question 4

Solve the equation.
-$5 n ^ { 2 } - 50 n + 5 = 5 n ( n - 10 )$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 5 \}$ 
C)  $\{ - 5 \}$ 
D)  $\{ 0 \}$ 
A)  $\varnothing$ 
B)  $\{ 5 \}$ 
C)  $\{ - 5 \}$ 
D)  $\{ 0 \}$

Question 5

Find the function.
-If $P ( x ) = 5 x + 8$, find $P ( a )$

Accepted Answer

A)  $13 a$ 
B)  $5 a$ 
C)  $5 x + 8$ 
D)  $5 a + 8$ 
A)  $13 a$ 
B)  $5 a$ 
C)  $5 x + 8$ 
D)  $5 a + 8$

Question 6

Fill in the blank with one of the words or phrases listed below.

-A shortcut method called may be used to divide a polynomial by a binomial of the form x - c.

Accepted Answer

A)  synthetic division 
B)  degree of a term 
C)  FOIL 
D)  factoring 
A)  synthetic division 
B)  degree of a term 
C)  FOIL 
D)  factoring

Question 7

Find all positive and negative integers b such that the trinomial is factorable.
-$$x ^ { 2 } + b x - 13$$

Accepted Answer

A)  14 
B)  $\pm 12$ 
C)  12 
D)  $\pm 14$ 
A)  14 
B)  $\pm 12$ 
C)  12 
D)  $\pm 14$

Question 8

Factor.
-$$x ^ { 3 } + 12 x ^ { 2 } + 36 x$$

Accepted Answer

A)  $x ( x + 6 ) ( x - 6 )$ 
B)  $x ( x + 6 ) ^ { 2 }$ 
C)  $x ( x - 6 ) ^ { 2 }$ 
D)  prime polynomial 
A)  $x ( x + 6 ) ( x - 6 )$ 
B)  $x ( x + 6 ) ^ { 2 }$ 
C)  $x ( x - 6 ) ^ { 2 }$ 
D)  prime polynomial

Question 9

Solve.
-A triangle is $2 \mathrm {~cm}$ wider than it is tall. The area is $12 \mathrm {~cm} ^ { 2 }$. Find the width (length of the base).

Accepted Answer

A)  $7 \mathrm {~cm}$ 
B)  $2 \mathrm {~cm}$ 
C)  $4 \mathrm {~cm}$ 
D)  $6 \mathrm {~cm}$ 
A)  $7 \mathrm {~cm}$ 
B)  $2 \mathrm {~cm}$ 
C)  $4 \mathrm {~cm}$ 
D)  $6 \mathrm {~cm}$

Question 10

Factor.
-$147 x ^ { 2 } - 48$

Accepted Answer

A)  $3 ( 7 x + 4 ) ^ { 2 }$ 
B)  $3 ( 7 x - 4 ) ^ { 2 }$ 
C)  $3 ( 7 x + 4 ) ( 7 x - 4 )$ 
D)  prime polynomial 
A)  $3 ( 7 x + 4 ) ^ { 2 }$ 
B)  $3 ( 7 x - 4 ) ^ { 2 }$ 
C)  $3 ( 7 x + 4 ) ( 7 x - 4 )$ 
D)  prime polynomial

Question 11

Find the function value.
-If $Q ( x ) = x ^ { 2 } - 5$, find $Q ( - 1 )$.

Accepted Answer

A)  36 
B)  1 
C)  $- 6$ 
D)  $- 4$ 
A)  36 
B)  1 
C)  $- 6$ 
D)  $- 4$

Question 12

Factor completely.
-$$x ^ { 2 } - 6 x + 9 - y ^ { 2 }$$

Accepted Answer

A)  $( x + 3 - y ) ^ { 2 }$ 
B)  $( x - 3 + y ) ( x - 3 - y )$ 
C)  $( x - 3 - y ) ^ { 2 }$ 
D)  $( x + 3 + y ) ( x + 3 - y )$ 
A)  $( x + 3 - y ) ^ { 2 }$ 
B)  $( x - 3 + y ) ( x - 3 - y )$ 
C)  $( x - 3 - y ) ^ { 2 }$ 
D)  $( x + 3 + y ) ( x + 3 - y )$

Question 13

Solve.
-The function $f ( x ) = 0.054 x ^ { 2 } + 0.66 x + 4.5$ can be used to approximate the number of computers sold during the years $1990 - 2000$, where $x$ is the number of years after 1990 and $f ( x )$ is the number of computers sold (in millions). Approximate the number of computers sold in 1998. Round your answer to the nearest tenth of a million.

Accepted Answer

A)  $11.8$ million 
B)  $13.2$ million 
C)  $4.5$ million 
D)  $10.2$ million 
A)  $11.8$ million 
B)  $13.2$ million 
C)  $4.5$ million 
D)  $10.2$ million

Question 14

Multiply.
-$$( 9 x - 7 ) ^ { 2 }$$

Accepted Answer

A)  $81 x ^ { 2 } + 49$ 
B)  $9 x ^ { 2 } - 126 x + 49$ 
C)  $9 x ^ { 2 } + 49$ 
D)  $81 x ^ { 2 } - 126 x + 49$ 
A)  $81 x ^ { 2 } + 49$ 
B)  $9 x ^ { 2 } - 126 x + 49$ 
C)  $9 x ^ { 2 } + 49$ 
D)  $81 x ^ { 2 } - 126 x + 49$

Question 15

Express the area of the shaded region as a polynomial. Factor the polynomial completely.
-

Accepted Answer

A)  $( x + 12 ) ^ { 2 }$ 
B)  $( x + 6 ) ( x - 6 )$ 
C)  $( x - 12 ) ^ { 2 }$ 
D)  $( x + 12 ) ( x - 12 )$ 
A)  $( x + 12 ) ^ { 2 }$ 
B)  $( x + 6 ) ( x - 6 )$ 
C)  $( x - 12 ) ^ { 2 }$ 
D)  $( x + 12 ) ( x - 12 )$

Question 16

Find the perimeter.
-

Accepted Answer

A)  $\left( 2 x ^ { 2 } + 16 x + 44 \right)$ units 
B)  $\left( x ^ { 2 } + 6 x + 22 \right)$ units 
C)  $\left( 2 x ^ { 2 } + 12 x + 22 \right)$ units 
D)  $\left( 2 x ^ { 2 } + 12 x + 44 \right)$ units 
A)  $\left( 2 x ^ { 2 } + 16 x + 44 \right)$ units 
B)  $\left( x ^ { 2 } + 6 x + 22 \right)$ units 
C)  $\left( 2 x ^ { 2 } + 12 x + 22 \right)$ units 
D)  $\left( 2 x ^ { 2 } + 12 x + 44 \right)$ units

Question 17

Multiply. Assume that variables used as exponents represent positive integers.
-$$\left( x ^ { a } + 7 y ^ { 2 b } \right) \left( x ^ { a } - 7 y ^ { 2 b } \right)$$

Accepted Answer

A)  $x ^ { 2 a } - 14 x ^ { a } y ^ { 2 b } - 49 y 4 b$ 
B)  $x ^ { 2 a } + 14 x ^ { a } y ^ { 2 b } - 49 y 4 b$ 
C)  $x ^ { 2 } a - 14 y 4 b$ 
D)  $x ^ { 2 a } - 49 y 4 b$ 
A)  $x ^ { 2 a } - 14 x ^ { a } y ^ { 2 b } - 49 y 4 b$ 
B)  $x ^ { 2 a } + 14 x ^ { a } y ^ { 2 b } - 49 y 4 b$ 
C)  $x ^ { 2 } a - 14 y 4 b$ 
D)  $x ^ { 2 a } - 49 y 4 b$

Question 18

Solve.
-The total revenues (in dollars) for a hot dog vendor selling $x$ hot dogs per day is given by the polynomial function $R ( x ) = 3 x$. Find the total revenue from selling 60 hot dogs per day.

Accepted Answer

A)  $\$ 18.00$ 
B)  $\$ 1080.00$ 
C)  $\$ 180.00$ 
D)  $\$ 1800.00$ 
A)  $\$ 18.00$ 
B)  $\$ 1080.00$ 
C)  $\$ 180.00$ 
D)  $\$ 1800.00$

Question 19

Solve the equation.
-$$x ^ { 3 } + 3 x ^ { 2 } = 108 x$$

Accepted Answer

A)  $\{ - 12,9 \}$ 
B)  $\{ 12 , - 9 \}$ 
C)  $\{ 12,0 , - 9 \}$ 
D)  $\{ - 12,0,9 \}$ 
A)  $\{ - 12,9 \}$ 
B)  $\{ 12 , - 9 \}$ 
C)  $\{ 12,0 , - 9 \}$ 
D)  $\{ - 12,0,9 \}$

Question 20

Factor completely.
-$$128 x ^ { 3 } y - 250 y ^ { 4 }$$

Accepted Answer

A)  $2 y ( 4 x - 5 y ) \left( 16 x ^ { 2 } + 20 x y + 25 y ^ { 2 } \right)$ 
B)  $2 y \left( 4 x + 5 y ^ { 2 } \right) \left( 16 x ^ { 2 } - 20 x y + 25 x y ^ { 2 } \right)$ 
C)  $2 y ( 64 x - 5 y ) \left( x ^ { 2 } + 20 x y + 25 y ^ { 2 } \right)$ 
D)  $\left( 8 x y - 10 y ^ { 2 } \right) \left( 16 x ^ { 2 } + 25 y ^ { 2 } \right)$ 
A)  $2 y ( 4 x - 5 y ) \left( 16 x ^ { 2 } + 20 x y + 25 y ^ { 2 } \right)$ 
B)  $2 y \left( 4 x + 5 y ^ { 2 } \right) \left( 16 x ^ { 2 } - 20 x y + 25 x y ^ { 2 } \right)$ 
C)  $2 y ( 64 x - 5 y ) \left( x ^ { 2 } + 20 x y + 25 y ^ { 2 } \right)$ 
D)  $\left( 8 x y - 10 y ^ { 2 } \right) \left( 16 x ^ { 2 } + 25 y ^ { 2 } \right)$

Multiply. - $( x - 5 ) ( 5 x - 4 )$

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. - $13 x ^ { 4 } + 7 x ^ { 3 } - 6 x - 3 y ^ { 5 }$

Solve. -The sum of two numbers is 17, and the sum of their squares is 145. Find the numbers.

Solve the equation. - $5 n ^ { 2 } - 50 n + 5 = 5 n ( n - 10 )$

Find the function. -If $P ( x ) = 5 x + 8$ , find $P ( a )$

Fill in the blank with one of the words or phrases listed below. -A shortcut method called may be used to divide a polynomial by a binomial of the form x - c.

Find all positive and negative integers b such that the trinomial is factorable. - $x ^ { 2 } + b x - 13$

Factor. - $x ^ { 3 } + 12 x ^ { 2 } + 36 x$

Solve. -A triangle is $2 \mathrm {~cm}$ wider than it is tall. The area is $12 \mathrm {~cm} ^ { 2 }$ . Find the width (length of the base). $Solve. -A triangle is 2 \mathrm {~cm} wider than it is tall. The area is 12 \mathrm {~cm} ^ { 2 } . Find the width (length of the base).$

Factor. - $147 x ^ { 2 } - 48$

Find the function value. -If $Q ( x ) = x ^ { 2 } - 5$ , find $Q ( - 1 )$ .

Factor completely. - $x ^ { 2 } - 6 x + 9 - y ^ { 2 }$

Multiply. - $( 9 x - 7 ) ^ { 2 }$

Express the area of the shaded region as a polynomial. Factor the polynomial completely. -

Find the perimeter. -

Multiply. Assume that variables used as exponents represent positive integers. - $\left( x ^ { a } + 7 y ^ { 2 b } \right) \left( x ^ { a } - 7 y ^ { 2 b } \right)$

Solve. -The total revenues (in dollars) for a hot dog vendor selling $x$ hot dogs per day is given by the polynomial function $R ( x ) = 3 x$ . Find the total revenue from selling 60 hot dogs per day.

Solve the equation. - $x ^ { 3 } + 3 x ^ { 2 } = 108 x$

Factor completely. - $128 x ^ { 3 } y - 250 y ^ { 4 }$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 5: Polynomials and Polynomial Functions

Multiply. - (x−5)(5x−4)( x - 5 ) ( 5 x - 4 )(x−5)(5x−4)

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. - 13x4+7x3−6x−3y513 x ^ { 4 } + 7 x ^ { 3 } - 6 x - 3 y ^ { 5 }13x4+7x3−6x−3y5

Solve. -The sum of two numbers is 17, and the sum of their squares is 145. Find the numbers.

Solve the equation. - 5n2−50n+5=5n(n−10)5 n ^ { 2 } - 50 n + 5 = 5 n ( n - 10 )5n2−50n+5=5n(n−10)

Find the function. -If P(x)=5x+8P ( x ) = 5 x + 8P(x)=5x+8 , find P(a)P ( a )P(a)