Question 1

Write $2.4 \times 10 ^ { - 4 }$ in standard notation.

Accepted Answer

A)  0.00024 
B)  2,400 
C)  0.0024 
D)  24,000 
A)  0.00024 
B)  2,400 
C)  0.0024 
D)  24,000

Question 2

Add. $\left( 5 a ^ { 2 } - 4 a - 5 \right) + \left( 6 a ^ { 2 } + 7 a + 2 \right)$

Accepted Answer

A)  $11 a ^ { 2 } + 3 a - 3$ 
B)  $11 a ^ { 2 } - 3 a + 3$ 
C)  $11 a ^ { 2 } + 3 a + 3$ 
D)  $11 a ^ { 2 } + 3 a - 5$ 
E)  $- 1 a ^ { 2 } + 3 a - 3$ 
A)  $11 a ^ { 2 } + 3 a - 3$ 
B)  $11 a ^ { 2 } - 3 a + 3$ 
C)  $11 a ^ { 2 } + 3 a + 3$ 
D)  $11 a ^ { 2 } + 3 a - 5$ 
E)  $- 1 a ^ { 2 } + 3 a - 3$

Question 3

An artist intends to paint a 84-square-foot mural on a wall that is 18 feet long and 10 feet high. If the artist wants to leave a border of uniform width, how wide should the border be? ( Hint: Let $w$ represent the width of the border. Then $18 - 2 w$ represents the length of the mural.)

Accepted Answer

A)  1 foot 
B)  6 foot 
C)  2 foot 
D)  14 foot 
E)  13 foot 
A)  1 foot 
B)  6 foot 
C)  2 foot 
D)  14 foot 
E)  13 foot

Question 4

For $5 x ^ { 2 } - 3 x + 4$ , 5 is called the __________ coefficient.

Accepted Answer

The answer of For \(5 x ^ { 2 }...

Question 5

Which of the following equations is a cubic equation?

Accepted Answer

A)  $2 x ^ { 3 } - 2 x ^ { 2 } - 5 = 0$ 
B)  $40 x ^ { 2 } - 5 x ^ { 4 } + 2 x ^ { 3 } = 0$ 
C)  $5 - x = 0$ 
D)  $40 x ^ { 2 } - 5 x = 2$ 
A)  $2 x ^ { 3 } - 2 x ^ { 2 } - 5 = 0$ 
B)  $40 x ^ { 2 } - 5 x ^ { 4 } + 2 x ^ { 3 } = 0$ 
C)  $5 - x = 0$ 
D)  $40 x ^ { 2 } - 5 x = 2$

Question 6

Solve: $x ^ { 3 } + 4 x ^ { 2 } - 32 x = 0$

Accepted Answer

A)  $\{ - 8,0,4 \}$ 
B)  $\{ - 8,4 \}$ 
C)  $\{ - 4,0,8 \}$ 
D)  $\{ - 4,8 \}$ 
A)  $\{ - 8,0,4 \}$ 
B)  $\{ - 8,4 \}$ 
C)  $\{ - 4,0,8 \}$ 
D)  $\{ - 4,8 \}$

Question 7

Factor the expression completely. If the expression is prime, so indicate. $64 x ^ { 4 } - 64$

Accepted Answer

A)  $64 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } - 1 \right)$ 
B)  $\left( 8 x ^ { 2 } - 8 \right) ( x + 1 ) ( 8 x - 8 )$ 
C)  $64 \left( x ^ { 2 } + 1 \right) ( x + 1 ) ( x - 1 )$ 
D)  $8 \left( 8 x ^ { 2 } - 1 \right) ( x + 1 ) ( x - 8 )$ 
E)  prime 
A)  $64 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } - 1 \right)$ 
B)  $\left( 8 x ^ { 2 } - 8 \right) ( x + 1 ) ( 8 x - 8 )$ 
C)  $64 \left( x ^ { 2 } + 1 \right) ( x + 1 ) ( x - 1 )$ 
D)  $8 \left( 8 x ^ { 2 } - 1 \right) ( x + 1 ) ( x - 8 )$ 
E)  prime

Question 8

Perform the indicated operation: $( 7 c + 3 d ) ( 7 c - 3 d )$

Accepted Answer

A)  $49 c ^ { 2 } - 9 d ^ { 2 }$ 
B)  $14 c ^ { 2 } - 6 d ^ { 2 }$ 
C)  $49 c ^ { 2 } - 2 c d - 9 d ^ { 2 }$ 
D)  $49 c ^ { 2 } - 42 c d + 9 d ^ { 2 }$ 
A)  $49 c ^ { 2 } - 9 d ^ { 2 }$ 
B)  $14 c ^ { 2 } - 6 d ^ { 2 }$ 
C)  $49 c ^ { 2 } - 2 c d - 9 d ^ { 2 }$ 
D)  $49 c ^ { 2 } - 42 c d + 9 d ^ { 2 }$

Question 9

Simplify the expression. $\frac { c ^ { 12 } c ^ { 5 } } { c ^ { - 7 } }$

Accepted Answer

A)  $c ^ { 10 }$ 
B)  $\frac { 1 } { 24 }$ 
C)  $\frac { 1 } { c ^ { 24 } }$ 
D)  $\frac { 1 } { c ^ { 10 } }$ 
E)  $c ^ { 24 }$ 
A)  $c ^ { 10 }$ 
B)  $\frac { 1 } { 24 }$ 
C)  $\frac { 1 } { c ^ { 24 } }$ 
D)  $\frac { 1 } { c ^ { 10 } }$ 
E)  $c ^ { 24 }$

Question 10

Write the number in standard notation. $8.5 \times 10 ^ { 2 }$

Accepted Answer

A)  0.85 
B)  8500 
C)  85 
D)  850 
E)  0.085 
A)  0.85 
B)  8500 
C)  85 
D)  850 
E)  0.085

Question 11

Simplify: $\frac { 5 x ^ { 0 } } { x ^ { - 3 } x ^ { - 4 } }$

Accepted Answer

A)  0 
B)  $\frac { x ^ { 7 } } { 5 }$ 
C)  $\frac { 5 } { x ^ { 12 } }$ 
D)  $5 x ^ { 7 }$ 
A)  0 
B)  $\frac { x ^ { 7 } } { 5 }$ 
C)  $\frac { 5 } { x ^ { 12 } }$ 
D)  $5 x ^ { 7 }$

Question 12

Simplify the expression. Write the answer using positive exponents. $m ^ { - 3 } m ^ { 2 } m ^ { - 8 }$

Accepted Answer

The answer of Simplify the expression. Write the answer using...

Question 13

Factor the expression completely. If the expression is prime, so indicate. $25 c ^ { 2 } g ^ { 2 } + h ^ { 2 }$

Accepted Answer

A)  $( 5 c g - h ) ( c g + h )$ 
B)  $( 25 c g - h ) ( 25 c g + h )$ 
C)  $5 \operatorname { cgh } ( 5 \operatorname { cg } + h )$ 
D)  $( 5 c g - h ) ( 5 c g + h )$ 
E)  prime 
A)  $( 5 c g - h ) ( c g + h )$ 
B)  $( 25 c g - h ) ( 25 c g + h )$ 
C)  $5 \operatorname { cgh } ( 5 \operatorname { cg } + h )$ 
D)  $( 5 c g - h ) ( 5 c g + h )$ 
E)  prime

Question 14

Write the number in scientific notation. 0.0073

Accepted Answer

A)  $7.3 \times 10 ^ { 3 }$ 
B)  $7.3 \times 10 ^ { - 2 }$ 
C)  $7.3 \times 10 ^ { 4 }$ 
D)  $7.3 \times 10 ^ { - 3 }$ 
E)  $7.3 \times 10 ^ { - 4 }$ 
A)  $7.3 \times 10 ^ { 3 }$ 
B)  $7.3 \times 10 ^ { - 2 }$ 
C)  $7.3 \times 10 ^ { 4 }$ 
D)  $7.3 \times 10 ^ { - 3 }$ 
E)  $7.3 \times 10 ^ { - 4 }$

Question 15

Factor the expression completely. $x ^ { 2 } + 10 x + 25 - y ^ { 2 }$ If the expression is prime, so indicate.

Accepted Answer

The answer of Factor the expression completely. \(x ^ {...

Question 16

In the exponential expression $x ^ { n }$ , x is called the _________.

Accepted Answer

The answer of In the exponential expression \(x ^ {...

Question 17

Factor the expression completely. If the expression is prime, so indicate. $7 ( x + y ) ^ { 2 } + ( x + y ) - 8$

Accepted Answer

A)  $( 7 x + 7 y + 8 ) ( x + y - 1 )$ 
B)  $( 7 x + 7 y - 8 ) ( x + y + 1 )$ 
C)  $( 8 x + 8 y + 7 ) ( x + y - 1 )$ 
D)  $( 8 x + 8 y - 7 ) ( x + y + 1 )$ 
E)  prime 
A)  $( 7 x + 7 y + 8 ) ( x + y - 1 )$ 
B)  $( 7 x + 7 y - 8 ) ( x + y + 1 )$ 
C)  $( 8 x + 8 y + 7 ) ( x + y - 1 )$ 
D)  $( 8 x + 8 y - 7 ) ( x + y + 1 )$ 
E)  prime

Question 18

The base of a triangle is 3 times its height. The area of the triangle is 92 square feet. If h represents the height of the triangle, write an equation that would find the height of the triangle.

Accepted Answer

A)  $92 = h ( 3 h )$ 
B)  $92 = \frac { 1 } { 2 } h ( 3 h )$ 
C)  $92 = \frac { 1 } { 2 } \left( \frac { h } { 3 } \right) ( h )$ 
D)  $92 = 2 h + 2 ( 3 h )$ 
A)  $92 = h ( 3 h )$ 
B)  $92 = \frac { 1 } { 2 } h ( 3 h )$ 
C)  $92 = \frac { 1 } { 2 } \left( \frac { h } { 3 } \right) ( h )$ 
D)  $92 = 2 h + 2 ( 3 h )$

Question 19

Multiply. $( x - y ) \left( x ^ { 2 } + x y + y ^ { 2 } \right)$

Accepted Answer

The answer of Multiply. \(( x - y ) \left(...

Question 20

Factor completely: $3 x ^ { 4 } - 48$

Accepted Answer

A)  $3 ( x - 2 ) ( x + 2 ) \left( x ^ { 2 } + 4 \right)$ 
B)  $3 ( x - 2 ) ( x + 2 ) ^ { 2 }$ 
C)  $3 \left( x ^ { 2 } - 4 \right) \left( x ^ { 2 } + 4 \right)$ 
D)  $3 \left( x ^ { 4 } - 16 \right)$ 
A)  $3 ( x - 2 ) ( x + 2 ) \left( x ^ { 2 } + 4 \right)$ 
B)  $3 ( x - 2 ) ( x + 2 ) ^ { 2 }$ 
C)  $3 \left( x ^ { 2 } - 4 \right) \left( x ^ { 2 } + 4 \right)$ 
D)  $3 \left( x ^ { 4 } - 16 \right)$

Write $2.4 \times 10 ^ { - 4 }$ in standard notation.

Add. $\left( 5 a ^ { 2 } - 4 a - 5 \right) + \left( 6 a ^ { 2 } + 7 a + 2 \right)$

An artist intends to paint a 84-square-foot mural on a wall that is 18 feet long and 10 feet high. If the artist wants to leave a border of uniform width, how wide should the border be? ( Hint: Let $w$ represent the width of the border. Then $18 - 2 w$ represents the length of the mural.)

For $5 x ^ { 2 } - 3 x + 4$ , 5 is called the __________ coefficient.

Which of the following equations is a cubic equation?

Solve: $x ^ { 3 } + 4 x ^ { 2 } - 32 x = 0$

Factor the expression completely. If the expression is prime, so indicate. $64 x ^ { 4 } - 64$

Perform the indicated operation: $( 7 c + 3 d ) ( 7 c - 3 d )$

Simplify the expression. $\frac { c ^ { 12 } c ^ { 5 } } { c ^ { - 7 } }$

Write the number in standard notation. $8.5 \times 10 ^ { 2 }$

Simplify: $\frac { 5 x ^ { 0 } } { x ^ { - 3 } x ^ { - 4 } }$

Simplify the expression. Write the answer using positive exponents. $m ^ { - 3 } m ^ { 2 } m ^ { - 8 }$

Factor the expression completely. If the expression is prime, so indicate. $25 c ^ { 2 } g ^ { 2 } + h ^ { 2 }$

Write the number in scientific notation. 0.0073

Factor the expression completely. $x ^ { 2 } + 10 x + 25 - y ^ { 2 }$ If the expression is prime, so indicate.

In the exponential expression $x ^ { n }$ , x is called the _________.

Factor the expression completely. If the expression is prime, so indicate. $7 ( x + y ) ^ { 2 } + ( x + y ) - 8$

The base of a triangle is 3 times its height. The area of the triangle is 92 square feet. If h represents the height of the triangle, write an equation that would find the height of the triangle.

Multiply. $( x - y ) \left( x ^ { 2 } + x y + y ^ { 2 } \right)$

Factor completely: $3 x ^ { 4 } - 48$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 5: Exponents, Polynomials, and Polynomial Functions

Write 2.4×10−42.4 \times 10 ^ { - 4 }2.4×10−4 in standard notation.

Add. (5a2−4a−5)+(6a2+7a+2)\left( 5 a ^ { 2 } - 4 a - 5 \right) + \left( 6 a ^ { 2 } + 7 a + 2 \right)(5a2−4a−5)+(6a2+7a+2)

For 5x2−3x+45 x ^ { 2 } - 3 x + 45x2−3x+4 , 5 is called the __________ coefficient.

Which of the following equations is a cubic equation?

Solve: x3+4x2−32x=0x ^ { 3 } + 4 x ^ { 2 } - 32 x = 0x3+4x2−32x=0

Factor the expression completely. If the expression is prime, so indicate. 64x4−6464 x ^ { 4 } - 6464x4−64

Perform the indicated operation: (7c+3d)(7c−3d)( 7 c + 3 d ) ( 7 c - 3 d )(7c+3d)(7c−3d)

Simplify the expression. c12c5c−7\frac { c ^ { 12 } c ^ { 5 } } { c ^ { - 7 } }c−7c12c5​

Write the number in standard notation. 8.5×1028.5 \times 10 ^ { 2 }8.5×102

Simplify: 5x0x−3x−4\frac { 5 x ^ { 0 } } { x ^ { - 3 } x ^ { - 4 } }x−3x−45x0​

Simplify the expression. Write the answer using positive exponents. m−3m2m−8m ^ { - 3 } m ^ { 2 } m ^ { - 8 }m−3m2m−8

Factor the expression completely. If the expression is prime, so indicate. 25c2g2+h225 c ^ { 2 } g ^ { 2 } + h ^ { 2 }25c2g2+h2

Write the number in scientific notation. 0.0073

Factor the expression completely. x2+10x+25−y2x ^ { 2 } + 10 x + 25 - y ^ { 2 }x2+10x+25−y2 If the expression is prime, so indicate.

In the exponential expression xnx ^ { n }xn , x is called the _________.

Factor the expression completely. If the expression is prime, so indicate. 7(x+y)2+(x+y)−87 ( x + y ) ^ { 2 } + ( x + y ) - 87(x+y)2+(x+y)−8

The base of a triangle is 3 times its height. The area of the triangle is 92 square feet. If h represents the height of the triangle, write an equation that would find the height of the triangle.

Multiply. (x−y)(x2+xy+y2)( x - y ) \left( x ^ { 2 } + x y + y ^ { 2 } \right)(x−y)(x2+xy+y2)

Factor completely: 3x4−483 x ^ { 4 } - 483x4−48

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Write $2.4 \times 10 ^ { - 4 }$ in standard notation.

Add. $\left( 5 a ^ { 2 } - 4 a - 5 \right) + \left( 6 a ^ { 2 } + 7 a + 2 \right)$

For $5 x ^ { 2 } - 3 x + 4$ , 5 is called the __________ coefficient.

Solve: $x ^ { 3 } + 4 x ^ { 2 } - 32 x = 0$

Factor the expression completely. If the expression is prime, so indicate. $64 x ^ { 4 } - 64$

Perform the indicated operation: $( 7 c + 3 d ) ( 7 c - 3 d )$

Simplify the expression. $\frac { c ^ { 12 } c ^ { 5 } } { c ^ { - 7 } }$

Write the number in standard notation. $8.5 \times 10 ^ { 2 }$

Simplify: $\frac { 5 x ^ { 0 } } { x ^ { - 3 } x ^ { - 4 } }$

Simplify the expression. Write the answer using positive exponents. $m ^ { - 3 } m ^ { 2 } m ^ { - 8 }$

Factor the expression completely. If the expression is prime, so indicate. $25 c ^ { 2 } g ^ { 2 } + h ^ { 2 }$

Factor the expression completely. $x ^ { 2 } + 10 x + 25 - y ^ { 2 }$ If the expression is prime, so indicate.

In the exponential expression $x ^ { n }$ , x is called the _________.

Factor the expression completely. If the expression is prime, so indicate. $7 ( x + y ) ^ { 2 } + ( x + y ) - 8$

Multiply. $( x - y ) \left( x ^ { 2 } + x y + y ^ { 2 } \right)$

Factor completely: $3 x ^ { 4 } - 48$