Question 1

The perimeter of a rectangle is 44 centimeters and the area is 112 square centimeters. Find the length and width of the rectangle.

Accepted Answer

A)  7 cm, 16 cm 
B)  6 cm, 16 cm 
C)  8 cm, 14 cm 
D)  7 cm, 13 cm 
E)  10 cm, 12 cm 
A)  7 cm, 16 cm 
B)  6 cm, 16 cm 
C)  8 cm, 14 cm 
D)  7 cm, 13 cm 
E)  10 cm, 12 cm

Question 2

Use the difference of squares pattern to factor the polynomial. $1 - 81 n ^ { 2 }$

Accepted Answer

( 1 @#LAT-DLM& 9 n )

Question 3

Set up an equation and solve the problem. The total surface area of a right circular cylinder is 100 $\pi$ square centimeters. If a radius of the base and the altitude of the cylinder are the same length, find the length of a radius. __________ centimeters

Accepted Answer

The answer of Set up an equation and solve the...

Question 4

Solve the equation. $5 x ^ { 2 } + 26 x + 5 = 0$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(5 x ^ {...

Question 5

Solve the equation. $8 p ^ { 2 } = - 32 p$

Accepted Answer

A)  $\{ 4,0 \}$ 
B)  $\{ 1,0 \}$ 
C)  $\{ - 1,0 \}$ 
D)  $\{ 4 \}$ 
E)  $\{ - 4,0 \}$ 
A)  $\{ 4,0 \}$ 
B)  $\{ 1,0 \}$ 
C)  $\{ - 1,0 \}$ 
D)  $\{ 4 \}$ 
E)  $\{ - 4,0 \}$

Question 6

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $x ^ { 2 } + 49 y ^ { 2 }$

Accepted Answer

The answer of Factor the polynomial completely. Don t forget...

Question 7

Set up an equation and solve the problem. 12 times the square of a number equals 588. Find the number.

Accepted Answer

A)  $-$ 49 or 49 
B)  $-$ 8 or 8 
C)  $-$ 7 or 7 
D)  0 
E)  none of these 
A)  $-$ 49 or 49 
B)  $-$ 8 or 8 
C)  $-$ 7 or 7 
D)  0 
E)  none of these

Question 8

Find two consecutive positive odd whole numbers whose product is 99. Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Find two consecutive positive odd whole numbers...

Question 9

Factor the trinomial completely. $68 y ^ { 2 } + y - 4$

Accepted Answer

A)  (4 y + 1)(17 y $-$ 5) 
B)  (4 y + 1)(17 y $-$ 4) 
C)  (4 y $-$ 1)(17 y + 4) 
D)  (4 y $-$ 1)(17 y $-$ 4) 
E)  not factorable 
A)  (4 y + 1)(17 y $-$ 5) 
B)  (4 y + 1)(17 y $-$ 4) 
C)  (4 y $-$ 1)(17 y + 4) 
D)  (4 y $-$ 1)(17 y $-$ 4) 
E)  not factorable

Question 10

The length of a rectangular sheet of paper is 1centimeter more than twice its width and the area of the rectangle is 105 square centimeters. Find the length of the rectangle.

Accepted Answer

A)  16 cm 
B)  13 cm 
C)  17 cm 
D)  15 cm 
A)  16 cm 
B)  13 cm 
C)  17 cm 
D)  15 cm

Question 11

Factor the following polynomial completely. $2 a ^ { 3 } - 18 a$

Accepted Answer

A)  $2 a ( a - 3 ) ( a + 3 )$ 
B)  $2 a \left( a ^ { 2 } - 9 \right)$ 
C)  $2 a \left( a ^ { 2 } + 9 \right)$ 
D)  $2 a ( a - 3 ) ( a - 3 )$ 
E)  none of these 
A)  $2 a ( a - 3 ) ( a + 3 )$ 
B)  $2 a \left( a ^ { 2 } - 9 \right)$ 
C)  $2 a \left( a ^ { 2 } + 9 \right)$ 
D)  $2 a ( a - 3 ) ( a - 3 )$ 
E)  none of these

Question 12

Use the difference of squares pattern to factor the polynomial. $1 - 9 n ^ { 2 }$

Accepted Answer

A)  (1 $-$ 3 n ) (1 + 3 n ) 
B)  (1 $-$ 3 n ) (1 + 9 n ) 
C)  (1 $-$ 9 n ) (1 + 3 n ) 
D)  (1 $-$ 3 n ) 
E)  none of these 
A)  (1 $-$ 3 n ) (1 + 3 n ) 
B)  (1 $-$ 3 n ) (1 + 9 n ) 
C)  (1 $-$ 9 n ) (1 + 3 n ) 
D)  (1 $-$ 3 n ) 
E)  none of these

Question 13

Find the greatest common factor of the given expression. $28 y \text { and } 32 y a$

Accepted Answer

A)  $4 y$ 
B)  $8 a$ 
C)  $7 y$ 
D)  $4 y a$ 
A)  $4 y$ 
B)  $8 a$ 
C)  $7 y$ 
D)  $4 y a$

Question 14

Choose the correct solution set. $4 x ^ { 2 } + 25 x - 21 = 0$

Accepted Answer

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

Question 15

Factor the trinomial completely. $2 x ^ { 2 } + 3 x + 1$

Accepted Answer

A)  $( 2 x + 2 ) ( x + 1 )$ 
B)  $( 2 x - 1 ) ( x - 1 )$ 
C)  $( x + 1 ) ( 2 x + 1 )$ 
D)  $( 2 x + 1 ) ( x + 1 )$ 
E)  not factorable 
A)  $( 2 x + 2 ) ( x + 1 )$ 
B)  $( 2 x - 1 ) ( x - 1 )$ 
C)  $( x + 1 ) ( 2 x + 1 )$ 
D)  $( 2 x + 1 ) ( x + 1 )$ 
E)  not factorable

Question 16

Solve the equation. $40 x ^ { 2 } + 6 x - 27 = 0$

Accepted Answer

The answer of Solve the equation. \(40 x ^ {...

Question 17

A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 13 inches by 9 inches in order to reduce the size of the paper to an area of 32 square inches. Find the width of the strip.

Accepted Answer

A)  3.0 in. 
B)  3.5 in. 
C)  1.5 in. 
D)  2.5 in. 
E)  2.0 in. 
A)  3.0 in. 
B)  3.5 in. 
C)  1.5 in. 
D)  2.5 in. 
E)  2.0 in.

Question 18

Solve the equation. $14 y ^ { 2 } + 23 y = - 3$

Accepted Answer

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

Question 19

Suppose that one leg of a right triangle is 5 feet shorter than the other leg. The hypotenuse is 5 feet longer than the longer leg. Find the lengths of all three sides of the right triangle.

Accepted Answer

A)  17 feet, 22 feet, 27 feet 
B)  15 feet, 20 feet, 25 feet 
C)  13 feet, 21 feet, 26 feet 
D)  13 feet, 22 feet, 25 feet 
A)  17 feet, 22 feet, 27 feet 
B)  15 feet, 20 feet, 25 feet 
C)  13 feet, 21 feet, 26 feet 
D)  13 feet, 22 feet, 25 feet

Question 20

For binomials of the form $x ^ { 2 } - a ^ { 2 } = 0$ , where $a \neq 0$ , there will be a negative answer and a positive answer.

Accepted Answer

A) True 
 B)False

The perimeter of a rectangle is 44 centimeters and the area is 112 square centimeters. Find the length and width of the rectangle.

Use the difference of squares pattern to factor the polynomial. $1 - 81 n ^ { 2 }$

Set up an equation and solve the problem. The total surface area of a right circular cylinder is 100 $\pi$ square centimeters. If a radius of the base and the altitude of the cylinder are the same length, find the length of a radius. __________ centimeters

Solve the equation. $5 x ^ { 2 } + 26 x + 5 = 0$ Please enter your answer as two numbers, separated by a comma.

Solve the equation. $8 p ^ { 2 } = - 32 p$

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $x ^ { 2 } + 49 y ^ { 2 }$

Set up an equation and solve the problem. 12 times the square of a number equals 588. Find the number.

Find two consecutive positive odd whole numbers whose product is 99. Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. $68 y ^ { 2 } + y - 4$

The length of a rectangular sheet of paper is 1centimeter more than twice its width and the area of the rectangle is 105 square centimeters. Find the length of the rectangle.

Factor the following polynomial completely. $2 a ^ { 3 } - 18 a$

Use the difference of squares pattern to factor the polynomial. $1 - 9 n ^ { 2 }$

Find the greatest common factor of the given expression. $28 y \text { and } 32 y a$

Choose the correct solution set. $4 x ^ { 2 } + 25 x - 21 = 0$

Factor the trinomial completely. $2 x ^ { 2 } + 3 x + 1$

Solve the equation. $40 x ^ { 2 } + 6 x - 27 = 0$

A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 13 inches by 9 inches in order to reduce the size of the paper to an area of 32 square inches. Find the width of the strip.

Solve the equation. $14 y ^ { 2 } + 23 y = - 3$

Suppose that one leg of a right triangle is 5 feet shorter than the other leg. The hypotenuse is 5 feet longer than the longer leg. Find the lengths of all three sides of the right triangle.

For binomials of the form $x ^ { 2 } - a ^ { 2 } = 0$ , where $a \neq 0$ , there will be a negative answer and a positive answer.

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

The perimeter of a rectangle is 44 centimeters and the area is 112 square centimeters. Find the length and width of the rectangle.

Use the difference of squares pattern to factor the polynomial. 1−81n21 - 81 n ^ { 2 }1−81n2

Set up an equation and solve the problem. The total surface area of a right circular cylinder is 100 π\piπ square centimeters. If a radius of the base and the altitude of the cylinder are the same length, find the length of a radius. __________ centimeters

Solve the equation. 5x2+26x+5=05 x ^ { 2 } + 26 x + 5 = 05x2+26x+5=0 Please enter your answer as two numbers, separated by a comma.

Solve the equation. 8p2=−32p8 p ^ { 2 } = - 32 p8p2=−32p

Factor the polynomial completely. Don t forget to look for a common monomial factor first. x2+49y2x ^ { 2 } + 49 y ^ { 2 }x2+49y2

Set up an equation and solve the problem. 12 times the square of a number equals 588. Find the number.

Find two consecutive positive odd whole numbers whose product is 99. Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. 68y2+y−468 y ^ { 2 } + y - 468y2+y−4

The length of a rectangular sheet of paper is 1centimeter more than twice its width and the area of the rectangle is 105 square centimeters. Find the length of the rectangle.

Factor the following polynomial completely. 2a3−18a2 a ^ { 3 } - 18 a2a3−18a

Use the difference of squares pattern to factor the polynomial. 1−9n21 - 9 n ^ { 2 }1−9n2

Find the greatest common factor of the given expression. 28y and 32ya28 y \text { and } 32 y a28y and 32ya

Choose the correct solution set. 4x2+25x−21=04 x ^ { 2 } + 25 x - 21 = 04x2+25x−21=0

Factor the trinomial completely. 2x2+3x+12 x ^ { 2 } + 3 x + 12x2+3x+1

Solve the equation. 40x2+6x−27=040 x ^ { 2 } + 6 x - 27 = 040x2+6x−27=0

A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 13 inches by 9 inches in order to reduce the size of the paper to an area of 32 square inches. Find the width of the strip.

Solve the equation. 14y2+23y=−314 y ^ { 2 } + 23 y = - 314y2+23y=−3

Suppose that one leg of a right triangle is 5 feet shorter than the other leg. The hypotenuse is 5 feet longer than the longer leg. Find the lengths of all three sides of the right triangle.

For binomials of the form x2−a2=0x ^ { 2 } - a ^ { 2 } = 0x2−a2=0 , where a≠0a \neq 0a=0 , there will be a negative answer and a positive answer.

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

Use the difference of squares pattern to factor the polynomial. $1 - 81 n ^ { 2 }$

Set up an equation and solve the problem. The total surface area of a right circular cylinder is 100 $\pi$ square centimeters. If a radius of the base and the altitude of the cylinder are the same length, find the length of a radius. __________ centimeters

Solve the equation. $5 x ^ { 2 } + 26 x + 5 = 0$ Please enter your answer as two numbers, separated by a comma.

Solve the equation. $8 p ^ { 2 } = - 32 p$

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $x ^ { 2 } + 49 y ^ { 2 }$

Factor the trinomial completely. $68 y ^ { 2 } + y - 4$

Factor the following polynomial completely. $2 a ^ { 3 } - 18 a$

Use the difference of squares pattern to factor the polynomial. $1 - 9 n ^ { 2 }$

Find the greatest common factor of the given expression. $28 y \text { and } 32 y a$

Choose the correct solution set. $4 x ^ { 2 } + 25 x - 21 = 0$

Factor the trinomial completely. $2 x ^ { 2 } + 3 x + 1$

Solve the equation. $40 x ^ { 2 } + 6 x - 27 = 0$

Solve the equation. $14 y ^ { 2 } + 23 y = - 3$

For binomials of the form $x ^ { 2 } - a ^ { 2 } = 0$ , where $a \neq 0$ , there will be a negative answer and a positive answer.