Question 1

Factor the following polynomial completely. $35 u ^ { 2 } + 3 u v - 2 v ^ { 2 }$

Accepted Answer

A)  $( 5 u + v ) ( 7 u + 2 v )$ 
B)  $( 5 u - v ) ( 7 u + 2 v )$ 
C)  $( 5 u - v ) ( 7 u - 2 v )$ 
D)  none of these 
A)  $( 5 u + v ) ( 7 u + 2 v )$ 
B)  $( 5 u - v ) ( 7 u + 2 v )$ 
C)  $( 5 u - v ) ( 7 u - 2 v )$ 
D)  none of these

Question 2

Solve the equation. $p ( 5 p - 20 ) - 5 ( 5 p - 20 ) = 0$

Accepted Answer

A)  { 5, 4 } 
B)  { $-$ 5, 4 } 
C)  { $-$ 5, $-$ 4 } 
D)  { 5, $-$ 4 } 
A)  { 5, 4 } 
B)  { $-$ 5, 4 } 
C)  { $-$ 5, $-$ 4 } 
D)  { 5, $-$ 4 }

Question 3

Set up an equation and solve the problem. The sum of the areas of two circles is 160 $\pi$ square meters. Find the length of a radius of the smaller circle if one of them is 3 times as long as the other.

Accepted Answer

A)  16 meters 
B)  3 meters 
C)  5 meters 
D)  4 meters 
E)  none of these 
A)  16 meters 
B)  3 meters 
C)  5 meters 
D)  4 meters 
E)  none of these

Question 4

The square of a number equals 20 times that number. Find the number. If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of The square of a number equals 20...

Question 5

Solve the equation. $12 x - x ^ { 2 } = 0$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(12 x - x...

Question 6

Solve the equation. $15 x ^ { 2 } + 11 x + 2 = 0$

Accepted Answer

The answer of Solve the equation. \(15 x ^ {...

Question 7

Factor the polynomial completely. $4 y ( d + 2 ) + 3 e ( d + 2 )$

Accepted Answer

A)  $( 4 y + 3 e ) ( d + 24 )$ 
B)  $4 y + 3 e ( d + 2 )$ 
C)  $( 4 y + 3 e ) ( d + 2 )$ 
A)  $( 4 y + 3 e ) ( d + 24 )$ 
B)  $4 y + 3 e ( d + 2 )$ 
C)  $( 4 y + 3 e ) ( d + 2 )$

Question 8

Set up an equation and solve the problem. The area of a triangle is 12.5 square feet. If one side of the triangle and the altitude to that side are of equal length, find the length.

Accepted Answer

A)  6 feet 
B)  4 feet 
C)  7 feet 
D)  5 feet 
E)  none of these 
A)  6 feet 
B)  4 feet 
C)  7 feet 
D)  5 feet 
E)  none of these

Question 9

Solve the equation. Write your answer in simplest form. $9 p ^ { 2 } + 54 p = 0$ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. Write your answer in...

Question 10

Solve the equation. Write your answer in simplest form. $y ( 13 y - 52 ) - 3 ( 13 y - 52 ) = 0$ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. Write your answer in...

Question 11

Set up an equation and solve the problem. The area of a triangle is 40.5 square feet. If one side of the triangle and the altitude to that side are of equal length, find the length.

Accepted Answer

A)  10 feet 
B)  9 feet 
C)  11 feet 
D)  8 feet 
E)  none of these 
A)  10 feet 
B)  9 feet 
C)  11 feet 
D)  8 feet 
E)  none of these

Question 12

Solve the equation. $x ^ { 2 } + 12 x + 27 = 0$

Accepted Answer

A)  {-9, 3} 
B)  {9, 3} 
C)  {12, 27} 
D)  {9, -3} 
E)  {-9, -3} 
A)  {-9, 3} 
B)  {9, 3} 
C)  {12, 27} 
D)  {9, -3} 
E)  {-9, -3}

Question 13

The first step is solving the equation $2 x ^ { 2 } + 13 x - 2 = 8$ is to make the equation equal to zero.

Accepted Answer

A) True 
 B)False

Question 14

Solve the equation. $10 x ^ { 2 } - 29 x + 10 = 0$

Accepted Answer

A)  $\left\{ \frac { 2 } { 5 } , - \frac { 5 } { 2 } \right\}$ 
B)  $\left\{ \frac { 5 } { 2 } \right\}$ 
C)  $\left\{ \frac { 2 } { 5 } , \frac { 5 } { 2 } \right\}$ 
D)  $\left\{ \frac { 2 } { 5 } \right\}$ 
E)  $\left\{ - \frac { 2 } { 5 } , \frac { 5 } { 2 } \right\}$ 
A)  $\left\{ \frac { 2 } { 5 } , - \frac { 5 } { 2 } \right\}$ 
B)  $\left\{ \frac { 5 } { 2 } \right\}$ 
C)  $\left\{ \frac { 2 } { 5 } , \frac { 5 } { 2 } \right\}$ 
D)  $\left\{ \frac { 2 } { 5 } \right\}$ 
E)  $\left\{ - \frac { 2 } { 5 } , \frac { 5 } { 2 } \right\}$

Question 15

Solve the equation. $3 y ( 3 y + 3 ) = 10$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 7 } , \frac { 4 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 3 } , \frac { 2 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 7 } , \frac { 2 } { 7 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 3 } , \frac { 4 } { 3 } \right\}$ 
A)  $\left\{ - \frac { 1 } { 7 } , \frac { 4 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 3 } , \frac { 2 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 7 } , \frac { 2 } { 7 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 3 } , \frac { 4 } { 3 } \right\}$

Question 16

Solve the equation. $8 x ^ { 2 } - 2 x - 21 = 0$

Accepted Answer

A)  $\left\{ \frac { 3 } { 2 } , - \frac { 7 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 3 } { 2 } , \frac { 7 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 2 } , - \frac { 7 } { 4 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 2 } , \frac { 4 } { 7 } \right\}$ 
E)  $\left\{ \frac { 3 } { 2 } , \frac { 7 } { 4 } \right\}$ 
A)  $\left\{ \frac { 3 } { 2 } , - \frac { 7 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 3 } { 2 } , \frac { 7 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 2 } , - \frac { 7 } { 4 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 2 } , \frac { 4 } { 7 } \right\}$ 
E)  $\left\{ \frac { 3 } { 2 } , \frac { 7 } { 4 } \right\}$

Question 17

In an office building, a room contains 30 chairs. The number of chairs per row is 4 less than twice the number of rows. Find the number of rows.

Accepted Answer

A)  6 rows 
B)  5 rows 
C)  7 rows 
D)  3 rows 
A)  6 rows 
B)  5 rows 
C)  7 rows 
D)  3 rows

Question 18

Solve the equation. $25 y ( y + 1 ) = - 6$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 5 } , - \frac { 2 } { 5 } \right\}$ 
B)  $\left\{ \frac { 3 } { 5 } , - \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ - 3 , - \frac { 2 } { 5 } \right\}$ 
A)  $\left\{ - \frac { 3 } { 5 } , - \frac { 2 } { 5 } \right\}$ 
B)  $\left\{ \frac { 3 } { 5 } , - \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ - 3 , - \frac { 2 } { 5 } \right\}$

Question 19

Use the process of factoring by grouping to factor the polynomial. $7 x + 7 y + z x + z y$

Accepted Answer

A)  $( x + y ) ( 7 + z )$ 
B)  $( z + y ) ( 4 + x )$ 
C)  $( z + y ) ( 7 + x )$ 
D)  $( x + z ) ( 7 + y )$ 
E)  $( x + z ) ( 4 + y )$ 
A)  $( x + y ) ( 7 + z )$ 
B)  $( z + y ) ( 4 + x )$ 
C)  $( z + y ) ( 7 + x )$ 
D)  $( x + z ) ( 7 + y )$ 
E)  $( x + z ) ( 4 + y )$

Question 20

Solve the equation. $( 10 x - 1 ) ( 5 x - 4 ) = 0$

Accepted Answer

A)  $\left\{ \frac { 1 } { 10 } , \frac { 4 } { 5 } \right\}$ 
B)  $\left\{ \frac { 1 } { 10 } , - \frac { 4 } { 5 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 10 } , \frac { 4 } { 5 } \right\}$ 
D)  none of these 
A)  $\left\{ \frac { 1 } { 10 } , \frac { 4 } { 5 } \right\}$ 
B)  $\left\{ \frac { 1 } { 10 } , - \frac { 4 } { 5 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 10 } , \frac { 4 } { 5 } \right\}$ 
D)  none of these

Factor the following polynomial completely. $35 u ^ { 2 } + 3 u v - 2 v ^ { 2 }$

Solve the equation. $p ( 5 p - 20 ) - 5 ( 5 p - 20 ) = 0$

Set up an equation and solve the problem. The sum of the areas of two circles is 160 $\pi$ square meters. Find the length of a radius of the smaller circle if one of them is 3 times as long as the other.

The square of a number equals 20 times that number. Find the number. If there is more than one solution, separate your answers with commas.

Solve the equation. $12 x - x ^ { 2 } = 0$ Please enter your answer as two numbers, separated by a comma.

Solve the equation. $15 x ^ { 2 } + 11 x + 2 = 0$

Factor the polynomial completely. $4 y ( d + 2 ) + 3 e ( d + 2 )$

Set up an equation and solve the problem. The area of a triangle is 12.5 square feet. If one side of the triangle and the altitude to that side are of equal length, find the length.

Solve the equation. Write your answer in simplest form. $9 p ^ { 2 } + 54 p = 0$ If there is more than one solution, separate your answers with commas.

Solve the equation. Write your answer in simplest form. $y ( 13 y - 52 ) - 3 ( 13 y - 52 ) = 0$ If there is more than one solution, separate your answers with commas.

Set up an equation and solve the problem. The area of a triangle is 40.5 square feet. If one side of the triangle and the altitude to that side are of equal length, find the length.

Solve the equation. $x ^ { 2 } + 12 x + 27 = 0$

The first step is solving the equation $2 x ^ { 2 } + 13 x - 2 = 8$ is to make the equation equal to zero.

Solve the equation. $10 x ^ { 2 } - 29 x + 10 = 0$

Solve the equation. $3 y ( 3 y + 3 ) = 10$

Solve the equation. $8 x ^ { 2 } - 2 x - 21 = 0$

In an office building, a room contains 30 chairs. The number of chairs per row is 4 less than twice the number of rows. Find the number of rows.

Solve the equation. $25 y ( y + 1 ) = - 6$

Use the process of factoring by grouping to factor the polynomial. $7 x + 7 y + z x + z y$

Solve the equation. $( 10 x - 1 ) ( 5 x - 4 ) = 0$

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 7: Factoring, Solving Equations and Problem Solving

Factor the following polynomial completely. 35u2+3uv−2v235 u ^ { 2 } + 3 u v - 2 v ^ { 2 }35u2+3uv−2v2

Solve the equation. p(5p−20)−5(5p−20)=0p ( 5 p - 20 ) - 5 ( 5 p - 20 ) = 0p(5p−20)−5(5p−20)=0

Set up an equation and solve the problem. The sum of the areas of two circles is 160 π\piπ square meters. Find the length of a radius of the smaller circle if one of them is 3 times as long as the other.

The square of a number equals 20 times that number. Find the number. If there is more than one solution, separate your answers with commas.

Solve the equation. 12x−x2=012 x - x ^ { 2 } = 012x−x2=0 Please enter your answer as two numbers, separated by a comma.

Solve the equation. 15x2+11x+2=015 x ^ { 2 } + 11 x + 2 = 015x2+11x+2=0

Factor the polynomial completely. 4y(d+2)+3e(d+2)4 y ( d + 2 ) + 3 e ( d + 2 )4y(d+2)+3e(d+2)

Set up an equation and solve the problem. The area of a triangle is 12.5 square feet. If one side of the triangle and the altitude to that side are of equal length, find the length.

Solve the equation. Write your answer in simplest form. 9p2+54p=09 p ^ { 2 } + 54 p = 09p2+54p=0 If there is more than one solution, separate your answers with commas.

Solve the equation. Write your answer in simplest form. y(13y−52)−3(13y−52)=0y ( 13 y - 52 ) - 3 ( 13 y - 52 ) = 0y(13y−52)−3(13y−52)=0 If there is more than one solution, separate your answers with commas.

Set up an equation and solve the problem. The area of a triangle is 40.5 square feet. If one side of the triangle and the altitude to that side are of equal length, find the length.

Solve the equation. x2+12x+27=0x ^ { 2 } + 12 x + 27 = 0x2+12x+27=0

The first step is solving the equation 2x2+13x−2=82 x ^ { 2 } + 13 x - 2 = 82x2+13x−2=8 is to make the equation equal to zero.

Solve the equation. 10x2−29x+10=010 x ^ { 2 } - 29 x + 10 = 010x2−29x+10=0

Solve the equation. 3y(3y+3)=103 y ( 3 y + 3 ) = 103y(3y+3)=10

Solve the equation. 8x2−2x−21=08 x ^ { 2 } - 2 x - 21 = 08x2−2x−21=0

In an office building, a room contains 30 chairs. The number of chairs per row is 4 less than twice the number of rows. Find the number of rows.

Solve the equation. 25y(y+1)=−625 y ( y + 1 ) = - 625y(y+1)=−6

Use the process of factoring by grouping to factor the polynomial. 7x+7y+zx+zy7 x + 7 y + z x + z y7x+7y+zx+zy

Solve the equation. (10x−1)(5x−4)=0( 10 x - 1 ) ( 5 x - 4 ) = 0(10x−1)(5x−4)=0

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Factor the following polynomial completely. $35 u ^ { 2 } + 3 u v - 2 v ^ { 2 }$

Solve the equation. $p ( 5 p - 20 ) - 5 ( 5 p - 20 ) = 0$

Set up an equation and solve the problem. The sum of the areas of two circles is 160 $\pi$ square meters. Find the length of a radius of the smaller circle if one of them is 3 times as long as the other.

Solve the equation. $12 x - x ^ { 2 } = 0$ Please enter your answer as two numbers, separated by a comma.

Solve the equation. $15 x ^ { 2 } + 11 x + 2 = 0$

Factor the polynomial completely. $4 y ( d + 2 ) + 3 e ( d + 2 )$

Solve the equation. Write your answer in simplest form. $9 p ^ { 2 } + 54 p = 0$ If there is more than one solution, separate your answers with commas.

Solve the equation. Write your answer in simplest form. $y ( 13 y - 52 ) - 3 ( 13 y - 52 ) = 0$ If there is more than one solution, separate your answers with commas.

Solve the equation. $x ^ { 2 } + 12 x + 27 = 0$

The first step is solving the equation $2 x ^ { 2 } + 13 x - 2 = 8$ is to make the equation equal to zero.

Solve the equation. $10 x ^ { 2 } - 29 x + 10 = 0$

Solve the equation. $3 y ( 3 y + 3 ) = 10$

Solve the equation. $8 x ^ { 2 } - 2 x - 21 = 0$

Solve the equation. $25 y ( y + 1 ) = - 6$

Use the process of factoring by grouping to factor the polynomial. $7 x + 7 y + z x + z y$

Solve the equation. $( 10 x - 1 ) ( 5 x - 4 ) = 0$