Question 1

Solve the equation. $5 t ^ { 2 } + 34 t - 7 = 0$

Accepted Answer

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

Question 2

Solve the equation. $x ^ { 2 } - 3 x - 70 = 0$

Accepted Answer

A)  $\{ - 10,7 \}$ 
B)  $\{ 10 , - 7 \}$ 
C)  $\{ - 10 , - 7 \}$ 
D)  $\{ 10,7 \}$ 
E)  none of these 
A)  $\{ - 10,7 \}$ 
B)  $\{ 10 , - 7 \}$ 
C)  $\{ - 10 , - 7 \}$ 
D)  $\{ 10,7 \}$ 
E)  none of these B

Question 3

Factor the following trinomial completely. $x ^ { 2 } - 7 x + 12$

Accepted Answer

A)  ( x $-$ 4)( x + 3) 
B)  ( x + 4)( x $-$ 3) 
C)  ( x $-$ 4)( x $-$ 3) 
D)  ( x + 4)( x + 3) 
A)  ( x $-$ 4)( x + 3) 
B)  ( x + 4)( x $-$ 3) 
C)  ( x $-$ 4)( x $-$ 3) 
D)  ( x + 4)( x + 3) C

Question 4

Solve the equation. $7 y ^ { 2 } + 8 y + 1 = 0$

Accepted Answer

A)  $\left\{ - 1 , - \frac { 1 } { 10 } \right\}$ 
B)  $\left\{ - 1 , - \frac { 1 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 11 } , - \frac { 1 } { 7 } \right\}$ 
A)  $\left\{ - 1 , - \frac { 1 } { 10 } \right\}$ 
B)  $\left\{ - 1 , - \frac { 1 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 11 } , - \frac { 1 } { 7 } \right\}$

Question 5

Factor the trinomial completely. $3 y ^ { 2 } + y + 4$

Accepted Answer

A)  (3 y $-$ 1)(11 y + 1) 
B)  (3 y $-$ 1)( y $-$ 4) 
C)  (3 y + 1)(2 y $-$ 4) 
D)  not factorable 
A)  (3 y $-$ 1)(11 y + 1) 
B)  (3 y $-$ 1)( y $-$ 4) 
C)  (3 y + 1)(2 y $-$ 4) 
D)  not factorable

Question 6

Factor the trinomial completely. $12 y ^ { 2 } + 12 y + 3$

Accepted Answer

A)  (6 y + 3)(2 y $-$ 1) 
B)  3 (2 y + 1)(2 y + 1) 
C)  3 (2 y $-$ 1)(2 y + 1) 
D)  3 (2 y + 1)( y + 1) 
E)  not factorable 
A)  (6 y + 3)(2 y $-$ 1) 
B)  3 (2 y + 1)(2 y + 1) 
C)  3 (2 y $-$ 1)(2 y + 1) 
D)  3 (2 y + 1)( y + 1) 
E)  not factorable

Question 7

Solve the equation. $10 x ^ { 2 } - 43 x - 9 = 0$

Accepted Answer

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

Question 8

Factor the following polynomial completely. $25 a ^ { 2 } + 5 a s - 2 s ^ { 2 }$

Accepted Answer

A)  $( 5 a - s ) ( 5 a + 2 s )$ 
B)  $( 5 a + s ) ( 5 a - 2 s )$ 
C)  $( 5 a - s ) ( 5 a - 2 s )$ 
D)  $( 5 a + s ) ( 5 a + 2 s )$ 
E)  none of these 
A)  $( 5 a - s ) ( 5 a + 2 s )$ 
B)  $( 5 a + s ) ( 5 a - 2 s )$ 
C)  $( 5 a - s ) ( 5 a - 2 s )$ 
D)  $( 5 a + s ) ( 5 a + 2 s )$ 
E)  none of these

Question 9

Solve the equation. $12 x ^ { 2 } + 11 x + 2 = 0$

Accepted Answer

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

Question 10

To solve an equation by factoring, organize all terms of the polynomial on the same side of the equation with zero on the other side.

Accepted Answer

A) True 
 B)False

Question 11

The length of a rectangular sheet of paper is 5 centimeters more than twice its width and the area of the rectangle is 75 square centimeters. Find the length of the rectangle.

Accepted Answer

A)  15 cm 
B)  17 cm 
C)  14 cm 
D)  13 cm 
E)  16 cm 
A)  15 cm 
B)  17 cm 
C)  14 cm 
D)  13 cm 
E)  16 cm

Question 12

Solve the equation. $a ^ { 3 } - 5 a ^ { 2 } - 14 a = 0$

Accepted Answer

A)  {2, 7, 0} 
B)  { $-$ 2, 7, 0} 
C)  {2, $-$ 7, 0} 
D)  none of these 
A)  {2, 7, 0} 
B)  { $-$ 2, 7, 0} 
C)  {2, $-$ 7, 0} 
D)  none of these

Question 13

Solve the equation. $x ^ { 2 } = 36$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

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

Question 14

Factor the trinomial completely. Indicate if it is not factorable using integers. $6 n ^ { 2 } + 3 n - 1$

Accepted Answer

The answer of Factor the trinomial completely. Indicate if it...

Question 15

Find two numbers whose product is 30 such that one of the numbers is 4 more than two times the other number.

Accepted Answer

A)  {10, 6}, {-6, -10} 
B)  {10, 3}, {-10, -3} 
C)  {10, 3}, {-6, -5} 
D)  {10, -5}, {-6, 3} 
E)  none of these 
A)  {10, 6}, {-6, -10} 
B)  {10, 3}, {-10, -3} 
C)  {10, 3}, {-6, -5} 
D)  {10, -5}, {-6, 3} 
E)  none of these

Question 16

Factor this trinomial completely. $6 x ^ { 2 } + x + 8$ Enter none if the trinomial is not factorable.

Accepted Answer

The answer of Factor this trinomial completely. \(6 x ^...

Question 17

Factor the following trinomial completely. $x ^ { 2 } + 7 x + 12$

Accepted Answer

A)  ( x + 4)( x $-$ 3) 
B)  ( x + 4)( x + 3) 
C)  ( x $-$ 4)( x + 3) 
D)  ( x $-$ 4)( x $-$ 3) 
A)  ( x + 4)( x $-$ 3) 
B)  ( x + 4)( x + 3) 
C)  ( x $-$ 4)( x + 3) 
D)  ( x $-$ 4)( x $-$ 3)

Question 18

Factor the polynomial completely. $5 y ^ { 2 } b ^ { 5 } + 4 y ^ { 8 } b ^ { 3 }$

Accepted Answer

The answer of Factor the polynomial completely. \(5 y ^...

Question 19

Set up an equation and solve the problem. 144 less than the square of a number equals zero. Find the number.

Accepted Answer

A)  { $-$ 14, 14 } 
B)  { $-$ 144, 144 } 
C)  0 
D)  { $-$ 12, 12 } 
E)  none of these 
A)  { $-$ 14, 14 } 
B)  { $-$ 144, 144 } 
C)  0 
D)  { $-$ 12, 12 } 
E)  none of these

Question 20

Solve the equation. $x ^ { 2 } - 324 = 0$

Accepted Answer

A)  $x = 334$ 
B)  $x = 1$ 
C)  $x = \pm 324$ 
D)  $x = \pm 18$ 
E)  none of these 
A)  $x = 334$ 
B)  $x = 1$ 
C)  $x = \pm 324$ 
D)  $x = \pm 18$ 
E)  none of these

Solve the equation. $5 t ^ { 2 } + 34 t - 7 = 0$

Solve the equation. $x ^ { 2 } - 3 x - 70 = 0$

Factor the following trinomial completely. $x ^ { 2 } - 7 x + 12$

Solve the equation. $7 y ^ { 2 } + 8 y + 1 = 0$

Factor the trinomial completely. $3 y ^ { 2 } + y + 4$

Factor the trinomial completely. $12 y ^ { 2 } + 12 y + 3$

Solve the equation. $10 x ^ { 2 } - 43 x - 9 = 0$

Factor the following polynomial completely. $25 a ^ { 2 } + 5 a s - 2 s ^ { 2 }$

Solve the equation. $12 x ^ { 2 } + 11 x + 2 = 0$

To solve an equation by factoring, organize all terms of the polynomial on the same side of the equation with zero on the other side.

The length of a rectangular sheet of paper is 5 centimeters more than twice its width and the area of the rectangle is 75 square centimeters. Find the length of the rectangle.

Solve the equation. $a ^ { 3 } - 5 a ^ { 2 } - 14 a = 0$

Solve the equation. $x ^ { 2 } = 36$ Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. Indicate if it is not factorable using integers. $6 n ^ { 2 } + 3 n - 1$

Find two numbers whose product is 30 such that one of the numbers is 4 more than two times the other number.

Factor this trinomial completely. $6 x ^ { 2 } + x + 8$ Enter none if the trinomial is not factorable.

Factor the following trinomial completely. $x ^ { 2 } + 7 x + 12$

Factor the polynomial completely. $5 y ^ { 2 } b ^ { 5 } + 4 y ^ { 8 } b ^ { 3 }$

Set up an equation and solve the problem. 144 less than the square of a number equals zero. Find the number.

Solve the equation. $x ^ { 2 } - 324 = 0$

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

Solve the equation. 5t2+34t−7=05 t ^ { 2 } + 34 t - 7 = 05t2+34t−7=0

Solve the equation. x2−3x−70=0x ^ { 2 } - 3 x - 70 = 0x2−3x−70=0

Factor the following trinomial completely. x2−7x+12x ^ { 2 } - 7 x + 12x2−7x+12

Solve the equation. 7y2+8y+1=07 y ^ { 2 } + 8 y + 1 = 07y2+8y+1=0

Factor the trinomial completely. 3y2+y+43 y ^ { 2 } + y + 43y2+y+4

Factor the trinomial completely. 12y2+12y+312 y ^ { 2 } + 12 y + 312y2+12y+3

Solve the equation. 10x2−43x−9=010 x ^ { 2 } - 43 x - 9 = 010x2−43x−9=0

Factor the following polynomial completely. 25a2+5as−2s225 a ^ { 2 } + 5 a s - 2 s ^ { 2 }25a2+5as−2s2

Solve the equation. 12x2+11x+2=012 x ^ { 2 } + 11 x + 2 = 012x2+11x+2=0

To solve an equation by factoring, organize all terms of the polynomial on the same side of the equation with zero on the other side.

The length of a rectangular sheet of paper is 5 centimeters more than twice its width and the area of the rectangle is 75 square centimeters. Find the length of the rectangle.

Solve the equation. a3−5a2−14a=0a ^ { 3 } - 5 a ^ { 2 } - 14 a = 0a3−5a2−14a=0

Solve the equation. x2=36x ^ { 2 } = 36x2=36 Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. Indicate if it is not factorable using integers. 6n2+3n−16 n ^ { 2 } + 3 n - 16n2+3n−1

Find two numbers whose product is 30 such that one of the numbers is 4 more than two times the other number.

Factor this trinomial completely. 6x2+x+86 x ^ { 2 } + x + 86x2+x+8 Enter none if the trinomial is not factorable.

Factor the following trinomial completely. x2+7x+12x ^ { 2 } + 7 x + 12x2+7x+12

Factor the polynomial completely. 5y2b5+4y8b35 y ^ { 2 } b ^ { 5 } + 4 y ^ { 8 } b ^ { 3 }5y2b5+4y8b3

Set up an equation and solve the problem. 144 less than the square of a number equals zero. Find the number.

Solve the equation. x2−324=0x ^ { 2 } - 324 = 0x2−324=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

Solve the equation. $5 t ^ { 2 } + 34 t - 7 = 0$

Solve the equation. $x ^ { 2 } - 3 x - 70 = 0$

Factor the following trinomial completely. $x ^ { 2 } - 7 x + 12$

Solve the equation. $7 y ^ { 2 } + 8 y + 1 = 0$

Factor the trinomial completely. $3 y ^ { 2 } + y + 4$

Factor the trinomial completely. $12 y ^ { 2 } + 12 y + 3$

Solve the equation. $10 x ^ { 2 } - 43 x - 9 = 0$

Factor the following polynomial completely. $25 a ^ { 2 } + 5 a s - 2 s ^ { 2 }$

Solve the equation. $12 x ^ { 2 } + 11 x + 2 = 0$

Solve the equation. $a ^ { 3 } - 5 a ^ { 2 } - 14 a = 0$

Solve the equation. $x ^ { 2 } = 36$ Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. Indicate if it is not factorable using integers. $6 n ^ { 2 } + 3 n - 1$

Factor this trinomial completely. $6 x ^ { 2 } + x + 8$ Enter none if the trinomial is not factorable.

Factor the following trinomial completely. $x ^ { 2 } + 7 x + 12$

Factor the polynomial completely. $5 y ^ { 2 } b ^ { 5 } + 4 y ^ { 8 } b ^ { 3 }$

Solve the equation. $x ^ { 2 } - 324 = 0$