Question 1

Factor the following polynomial completely. $2 a ^ { 4 } - 32$

Accepted Answer

A)  $2 ( a + 2 ) \left( a ^ { 2 } + 4 \right)$ 
B)  $( a - 2 ) ( a + 2 ) \left( a ^ { 2 } + 4 \right)$ 
C)  $2 ( a - 2 ) ( a + 2 ) \left( a ^ { 2 } + 4 \right)$ 
D)  none of these 
A)  $2 ( a + 2 ) \left( a ^ { 2 } + 4 \right)$ 
B)  $( a - 2 ) ( a + 2 ) \left( a ^ { 2 } + 4 \right)$ 
C)  $2 ( a - 2 ) ( a + 2 ) \left( a ^ { 2 } + 4 \right)$ 
D)  none of these

Question 2

Find two consecutive positive odd whole numbers whose product is 143.

Accepted Answer

A)  13, 15 
B)  11, 13 
C)  11, 12 
A)  13, 15 
B)  11, 13 
C)  11, 12

Question 3

Solve the equation. $16 y ( y + 1 ) = - 3$

Accepted Answer

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

Question 4

Solve the equation. $4 t ^ { 2 } - 12 t = 0$

Accepted Answer

A)  $\{ 3,0 \}$ 
B)  $\{ 3,4 \}$ 
C)  $\{ 12,0 \}$ 
D)  none of these 
A)  $\{ 3,0 \}$ 
B)  $\{ 3,4 \}$ 
C)  $\{ 12,0 \}$ 
D)  none of these

Question 5

Find the greatest common factor of the given expression. $15 z ^ { 4 } c ^ { 6 } , 10 z ^ { 3 } c ^ { 7 } \text { and } 55 z ^ { 6 } c ^ { 2 }$

Accepted Answer

A)  $2 c ^ { 5 }$ 
B)  $5 z c ^ { 4 }$ 
C)  $3 z ^ { 8 } c ^ { 2 }$ 
D)  $5 z ^ { 3 } c ^ { 2 }$ 
A)  $2 c ^ { 5 }$ 
B)  $5 z c ^ { 4 }$ 
C)  $3 z ^ { 8 } c ^ { 2 }$ 
D)  $5 z ^ { 3 } c ^ { 2 }$

Question 6

Solve the equation. $7 y ( 7 y + 3 ) = 4$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 7 } , \frac { 2 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 4 } { 9 } , \frac { 1 } { 9 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 9 } , \frac { 2 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 4 } { 7 } , \frac { 1 } { 7 } \right\}$ 
E)  $\left\{ \frac { 4 } { 7 } , - \frac { 1 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 7 } , \frac { 2 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 4 } { 9 } , \frac { 1 } { 9 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 9 } , \frac { 2 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 4 } { 7 } , \frac { 1 } { 7 } \right\}$ 
E)  $\left\{ \frac { 4 } { 7 } , - \frac { 1 } { 7 } \right\}$

Question 7

Solve the equation. $x ^ { 2 } + 6 x = 7$

Accepted Answer

A)  {1, 7} 
B)  {-1, -7} 
C)  {1, -7} 
D)  {-1, 7} 
E)  {6, 7} 
A)  {1, 7} 
B)  {-1, -7} 
C)  {1, -7} 
D)  {-1, 7} 
E)  {6, 7}

Question 8

Find three negative consecutive integers such that the product of the two smaller integers is 116 more than ten times the largest integer.

Accepted Answer

A)  -10, -9, -8 
B)  -8, -7, -6 
C)  -9, -8, -7 
D)  -6, -5, -4 
A)  -10, -9, -8 
B)  -8, -7, -6 
C)  -9, -8, -7 
D)  -6, -5, -4

Question 9

Set up an equation and solve the problem. 7 times the square of a number equals 175. Find the number. Please enter your answer as two numbers, separated by a comma.

Accepted Answer

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

Question 10

Solve the equation. $x ^ { 2 } - 2 x - 63 = 0$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(x ^ { 2...

Question 11

Find the greatest common factor of the given expressions. $45 x a , 20 x a ^ { 5 } \text { and } 85 x ^ { 2 } a$

Accepted Answer

The answer of Find the greatest common factor of the...

Question 12

Factor the trinomial completely. Indicate if it is not factorable using integers. $28 x ^ { 2 } - 144 x + 20$

Accepted Answer

4 ( 7 x @#LAT-DLM& 1

Question 13

Solve the equation. $16 x ^ { 2 } - 18 x - 9 = 0$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(16 x ^ {...

Question 14

Set up an equation and solve the problem. 81 less than the square of a number equals zero. Find the number. Please enter your answer as two numbers, separated by a comma.

Accepted Answer

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

Question 15

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $x ^ { 2 } + 25 y ^ { 2 }$

Accepted Answer

A)  $( x - 5 y ) ( x + 5 y )$ 
B)  $( y - 10 x ) ( x + 5 y )$ 
C)  $( x - 10 y ) ( x + 10 y )$ 
D)  $( y - 5 x ) ( x + 5 y )$ 
E)  not factorable 
A)  $( x - 5 y ) ( x + 5 y )$ 
B)  $( y - 10 x ) ( x + 5 y )$ 
C)  $( x - 10 y ) ( x + 10 y )$ 
D)  $( y - 5 x ) ( x + 5 y )$ 
E)  not factorable

Question 16

Factor the following trinomial completely. $x ^ { 2 } + 7 x y - 8 y ^ { 2 }$

Accepted Answer

( x @#LAT-DLM& y ) (

Question 17

Set up an equation and solve the problem. The difference of the areas of two squares is 6,912 square inches. Each side of the larger square is 7 times the length of a side of the smaller square. Find the length of a side of the larger square. __________ inches

Accepted Answer

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

Question 18

Solve the equation. $4 y ^ { 2 } + 24 y = 0$

Accepted Answer

A)  { $-$ 1, 0 } 
B)  { 1, 0 } 
C)  { 6, 0 } 
D)  { $-$ 6, 0 } 
E)  { 1 } 
A)  { $-$ 1, 0 } 
B)  { 1, 0 } 
C)  { 6, 0 } 
D)  { $-$ 6, 0 } 
E)  { 1 }

Question 19

The length of one leg of a right triangle is 1 centimeter more than the length of the other leg. The length of the hypotenuse is 5 centimeters. Find the lengths of the two legs.

Accepted Answer

A)  3 cm, 4 cm 
B)  1 cm, 2 cm 
C)  6 cm, 5 cm 
D)  5 cm, 6 cm 
A)  3 cm, 4 cm 
B)  1 cm, 2 cm 
C)  6 cm, 5 cm 
D)  5 cm, 6 cm

Question 20

Solve the equation. $21 ( z - 9 ) - z ( z - 9 ) = 0$

Accepted Answer

A)  $\{ - 21 , - 9 \}$ 
B)  $\{ 21,9 \}$ 
C)  $\{ 21 , - 9 \}$ 
D)  $\{ 21 \}$ 
E)  $\{ - 21,9 \}$ 
A)  $\{ - 21 , - 9 \}$ 
B)  $\{ 21,9 \}$ 
C)  $\{ 21 , - 9 \}$ 
D)  $\{ 21 \}$ 
E)  $\{ - 21,9 \}$

Factor the following polynomial completely. $2 a ^ { 4 } - 32$

Find two consecutive positive odd whole numbers whose product is 143.

Solve the equation. $16 y ( y + 1 ) = - 3$

Solve the equation. $4 t ^ { 2 } - 12 t = 0$

Find the greatest common factor of the given expression. $15 z ^ { 4 } c ^ { 6 } , 10 z ^ { 3 } c ^ { 7 } \text { and } 55 z ^ { 6 } c ^ { 2 }$

Solve the equation. $7 y ( 7 y + 3 ) = 4$

Solve the equation. $x ^ { 2 } + 6 x = 7$

Find three negative consecutive integers such that the product of the two smaller integers is 116 more than ten times the largest integer.

Set up an equation and solve the problem. 7 times the square of a number equals 175. Find the number. Please enter your answer as two numbers, separated by a comma.

Solve the equation. $x ^ { 2 } - 2 x - 63 = 0$ Please enter your answer as two numbers, separated by a comma.

Find the greatest common factor of the given expressions. $45 x a , 20 x a ^ { 5 } \text { and } 85 x ^ { 2 } a$

Factor the trinomial completely. Indicate if it is not factorable using integers. $28 x ^ { 2 } - 144 x + 20$

Solve the equation. $16 x ^ { 2 } - 18 x - 9 = 0$ Please enter your answer as two numbers, separated by a comma.

Set up an equation and solve the problem. 81 less than the square of a number equals zero. Find the number. Please enter your answer as two numbers, separated by a comma.

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $x ^ { 2 } + 25 y ^ { 2 }$

Factor the following trinomial completely. $x ^ { 2 } + 7 x y - 8 y ^ { 2 }$

Set up an equation and solve the problem. The difference of the areas of two squares is 6,912 square inches. Each side of the larger square is 7 times the length of a side of the smaller square. Find the length of a side of the larger square. __________ inches

Solve the equation. $4 y ^ { 2 } + 24 y = 0$

The length of one leg of a right triangle is 1 centimeter more than the length of the other leg. The length of the hypotenuse is 5 centimeters. Find the lengths of the two legs.

Solve the equation. $21 ( z - 9 ) - z ( z - 9 ) = 0$

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. 2a4−322 a ^ { 4 } - 322a4−32

Find two consecutive positive odd whole numbers whose product is 143.

Solve the equation. 16y(y+1)=−316 y ( y + 1 ) = - 316y(y+1)=−3

Solve the equation. 4t2−12t=04 t ^ { 2 } - 12 t = 04t2−12t=0

Find the greatest common factor of the given expression. 15z4c6,10z3c7 and 55z6c215 z ^ { 4 } c ^ { 6 } , 10 z ^ { 3 } c ^ { 7 } \text { and } 55 z ^ { 6 } c ^ { 2 }15z4c6,10z3c7 and 55z6c2

Solve the equation. 7y(7y+3)=47 y ( 7 y + 3 ) = 47y(7y+3)=4

Solve the equation. x2+6x=7x ^ { 2 } + 6 x = 7x2+6x=7

Find three negative consecutive integers such that the product of the two smaller integers is 116 more than ten times the largest integer.

Set up an equation and solve the problem. 7 times the square of a number equals 175. Find the number. Please enter your answer as two numbers, separated by a comma.

Solve the equation. x2−2x−63=0x ^ { 2 } - 2 x - 63 = 0x2−2x−63=0 Please enter your answer as two numbers, separated by a comma.

Find the greatest common factor of the given expressions. 45xa,20xa5 and 85x2a45 x a , 20 x a ^ { 5 } \text { and } 85 x ^ { 2 } a45xa,20xa5 and 85x2a

Factor the trinomial completely. Indicate if it is not factorable using integers. 28x2−144x+2028 x ^ { 2 } - 144 x + 2028x2−144x+20

Solve the equation. 16x2−18x−9=016 x ^ { 2 } - 18 x - 9 = 016x2−18x−9=0 Please enter your answer as two numbers, separated by a comma.

Set up an equation and solve the problem. 81 less than the square of a number equals zero. Find the number. Please enter your answer as two numbers, separated by a comma.

Factor the polynomial completely. Don t forget to look for a common monomial factor first. x2+25y2x ^ { 2 } + 25 y ^ { 2 }x2+25y2

Factor the following trinomial completely. x2+7xy−8y2x ^ { 2 } + 7 x y - 8 y ^ { 2 }x2+7xy−8y2

Set up an equation and solve the problem. The difference of the areas of two squares is 6,912 square inches. Each side of the larger square is 7 times the length of a side of the smaller square. Find the length of a side of the larger square. __________ inches

Solve the equation. 4y2+24y=04 y ^ { 2 } + 24 y = 04y2+24y=0

The length of one leg of a right triangle is 1 centimeter more than the length of the other leg. The length of the hypotenuse is 5 centimeters. Find the lengths of the two legs.

Solve the equation. 21(z−9)−z(z−9)=021 ( z - 9 ) - z ( z - 9 ) = 021(z−9)−z(z−9)=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. $2 a ^ { 4 } - 32$

Solve the equation. $16 y ( y + 1 ) = - 3$

Solve the equation. $4 t ^ { 2 } - 12 t = 0$

Find the greatest common factor of the given expression. $15 z ^ { 4 } c ^ { 6 } , 10 z ^ { 3 } c ^ { 7 } \text { and } 55 z ^ { 6 } c ^ { 2 }$

Solve the equation. $7 y ( 7 y + 3 ) = 4$

Solve the equation. $x ^ { 2 } + 6 x = 7$

Solve the equation. $x ^ { 2 } - 2 x - 63 = 0$ Please enter your answer as two numbers, separated by a comma.

Find the greatest common factor of the given expressions. $45 x a , 20 x a ^ { 5 } \text { and } 85 x ^ { 2 } a$

Factor the trinomial completely. Indicate if it is not factorable using integers. $28 x ^ { 2 } - 144 x + 20$

Solve the equation. $16 x ^ { 2 } - 18 x - 9 = 0$ Please enter your answer as two numbers, separated by a comma.

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $x ^ { 2 } + 25 y ^ { 2 }$

Factor the following trinomial completely. $x ^ { 2 } + 7 x y - 8 y ^ { 2 }$

Solve the equation. $4 y ^ { 2 } + 24 y = 0$

Solve the equation. $21 ( z - 9 ) - z ( z - 9 ) = 0$