Question 1

Write the number in standard notation. $3.3 \times 10 ^ { - 8 }$

Accepted Answer

A)  330,000,000 
B)  0.000000033 
C)  0.0000000033 
D)  33000000 
E)  0.0033 
A)  330,000,000 
B)  0.000000033 
C)  0.0000000033 
D)  33000000 
E)  0.0033

Question 2

Solve the equation. $2 x ^ { 2 } + 6 x = 0$, x = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

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

Question 3

Solve: $( x - 4 ) ( x + 3 ) = 8$

Accepted Answer

A)  $\{ - 3,4 \}$ 
B)  $\{ 5,4 \}$ 
C)  $\{ - 5,4 \}$ 
D)  $\{ - 4,5 \}$ 
A)  $\{ - 3,4 \}$ 
B)  $\{ 5,4 \}$ 
C)  $\{ - 5,4 \}$ 
D)  $\{ - 4,5 \}$

Question 4

Simplify the expression. $\left( \frac { a } { b ^ { 2 } } \right) ^ { 3 }$

Accepted Answer

A)  $\frac { a ^ { 3 } } { b ^ { 6 } }$ 
B)  $\frac { a ^ { 4 } } { b ^ { 5 } }$ 
C)  $\frac { b ^ { 6 } } { a ^ { 3 } }$ 
D)  $\frac { a ^ { 3 } } { b ^ { 5 } }$ 
E)  $\frac { a ^ { 6 } } { b ^ { 3 } }$ 
A)  $\frac { a ^ { 3 } } { b ^ { 6 } }$ 
B)  $\frac { a ^ { 4 } } { b ^ { 5 } }$ 
C)  $\frac { b ^ { 6 } } { a ^ { 3 } }$ 
D)  $\frac { a ^ { 3 } } { b ^ { 5 } }$ 
E)  $\frac { a ^ { 6 } } { b ^ { 3 } }$

Question 5

Perform the indicated operations. $\left( 4 x ^ { 2 } + 3 x - 3 \right) + \left( 4 x ^ { 2 } - 2 x - 2 \right) - \left( x ^ { 2 } + x + 6 \right)$

Accepted Answer

The answer of Perform the indicated operations. \(\left( 4 x...

Question 6

Factor the expression completely. If the expression is prime, so indicate. $- 13 m ^ { 2 } + m ^ { 4 } + 36$

Accepted Answer

A)  $( m + 3 ) ( m - 3 ) \left( m ^ { 2 } + 4 \right)$ 
B)  $( m - 2 ) ( m + 2 ) \left( m ^ { 2 } + 9 \right)$ 
C)  $( m + 3 ) ( m - 3 ) ( m + 2 ) ( m - 2 )$ 
D)  $( m + 3 ) ( m + 3 ) ( m - 2 ) ( m - 2 )$ 
E)  prime 
A)  $( m + 3 ) ( m - 3 ) \left( m ^ { 2 } + 4 \right)$ 
B)  $( m - 2 ) ( m + 2 ) \left( m ^ { 2 } + 9 \right)$ 
C)  $( m + 3 ) ( m - 3 ) ( m + 2 ) ( m - 2 )$ 
D)  $( m + 3 ) ( m + 3 ) ( m - 2 ) ( m - 2 )$ 
E)  prime

Question 7

The length of a rectangular ice-skating rink is 20 meters greater than twice its width. Find the width.  
$w$=__________ m

Accepted Answer

The answer of The length of a rectangular ice-skating rink...

Question 8

Factor the expression completely. If the expression is prime, so indicate. $27 x ^ { 3 } y ^ { 4 } - 8 y$

Accepted Answer

A)  $y ( 4 x y - 3 ) \left( 9 x ^ { 2 } y ^ { 2 } + 6 x y + 4 \right)$ 
B)  $y ( 3 x y - 2 ) \left( 9 x ^ { 2 } y ^ { 2 } + 6 x y + 4 \right)$ 
C)  $y ( 4 x y + 3 ) \left( 9 x ^ { 2 } y ^ { 2 } - 6 x y + 4 \right)$ 
D)  $y ( 3 x y + 2 ) \left( 9 x ^ { 2 } y ^ { 2 } - 6 x y + 4 \right)$ 
E)  prime 
A)  $y ( 4 x y - 3 ) \left( 9 x ^ { 2 } y ^ { 2 } + 6 x y + 4 \right)$ 
B)  $y ( 3 x y - 2 ) \left( 9 x ^ { 2 } y ^ { 2 } + 6 x y + 4 \right)$ 
C)  $y ( 4 x y + 3 ) \left( 9 x ^ { 2 } y ^ { 2 } - 6 x y + 4 \right)$ 
D)  $y ( 3 x y + 2 ) \left( 9 x ^ { 2 } y ^ { 2 } - 6 x y + 4 \right)$ 
E)  prime

Question 9

Factor the expression completely. $27 x ^ { 3 } y ^ { 4 } - 8 y$ If the expression is prime, so indicate.

Accepted Answer

The answer of Factor the expression completely. \(27 x ^...

Question 10

Perform the indicated operations. $( a - b ) ( a + b ) ( a - 6 b )$

Accepted Answer

The answer of Perform the indicated operations. \(( a -...

Question 11

In any factoring problem, always factor out any _________ factors first.

Accepted Answer

The answer of In any factoring problem, always factor out...

Question 12

Factor: $- 24 x ^ { 2 } + 70 x y + 66 y ^ { 2 }$

Accepted Answer

A)  $- 2 ( 4 x + 3 y ) ( 3 x - 11 y )$ 
B)  $- 2 ( 4 x - 3 y ) ( 3 x + 11 y )$ 
C)  $- 2 ( 2 x - 11 y ) ( 6 x + 3 y )$ 
D)  $- 2 ( 2 x + 11 y ) ( 6 x - 3 y )$ 
A)  $- 2 ( 4 x + 3 y ) ( 3 x - 11 y )$ 
B)  $- 2 ( 4 x - 3 y ) ( 3 x + 11 y )$ 
C)  $- 2 ( 2 x - 11 y ) ( 6 x + 3 y )$ 
D)  $- 2 ( 2 x + 11 y ) ( 6 x - 3 y )$

Question 13

If $f ( x ) = 2 x ^ { 2 } - 4 x - 7$ , find $f ( c + 5 )$.

Accepted Answer

A)  $2 c ^ { 2 } - 4 c + 23$ 
B)  $2 c ^ { 2 } + 16 c + 63$ 
C)  none of these 
D)  $2 c ^ { 2 } + 16 c + 23$ 
A)  $2 c ^ { 2 } - 4 c + 23$ 
B)  $2 c ^ { 2 } + 16 c + 63$ 
C)  none of these 
D)  $2 c ^ { 2 } + 16 c + 23$

Question 14

Simplify: $\left( 2 x ^ { - 3 } \right) ^ { - 4 }$

Accepted Answer

A)  $\frac { x ^ { 12 } } { 16 }$ 
B)  $2 x ^ { 12 }$ 
C)  $- 16 x ^ { 12 }$ 
D)  $- 8 x ^ { 12 }$ 
A)  $\frac { x ^ { 12 } } { 16 }$ 
B)  $2 x ^ { 12 }$ 
C)  $- 16 x ^ { 12 }$ 
D)  $- 8 x ^ { 12 }$

Question 15

Write the numbers in scientific notation and perform the operations. Give the answer in scientific notation and in standard notation. $( 85,000,000,000 ) ( 4,700,000,000 )$

Accepted Answer

A)  $3.995 \times 10 ^ { 19 } , \quad 39,950,000,000,000,000,000$ 
B)  $0.3995 \times 10 ^ { 20 } , \quad 3,995,000,000,000,000,000$ 
C)  $3.995 \times 10 ^ { 20 } , \quad 399,500,000,000,000,000,000$ 
D)  $0.3995 \times 10 ^ { 19 } , \quad 3,995,000,000,000,000,000$ 
E)  $3.995 \times 10 ^ { 18 } , \quad 3,995,000,000,000,000,000$ 
A)  $3.995 \times 10 ^ { 19 } , \quad 39,950,000,000,000,000,000$ 
B)  $0.3995 \times 10 ^ { 20 } , \quad 3,995,000,000,000,000,000$ 
C)  $3.995 \times 10 ^ { 20 } , \quad 399,500,000,000,000,000,000$ 
D)  $0.3995 \times 10 ^ { 19 } , \quad 3,995,000,000,000,000,000$ 
E)  $3.995 \times 10 ^ { 18 } , \quad 3,995,000,000,000,000,000$

Question 16

Find the product. $- 4 y z ( 3 y - z ) ( 2 y - z )$

Accepted Answer

A)  $- 24 y ^ { 3 } z + 20 y ^ { 2 } z ^ { 2 } + 4 y z ^ { 3 }$ 
B)  $- 24 y ^ { 3 } z + 20 y ^ { 2 } z ^ { 2 } - 4 y z ^ { 3 }$ 
C)  $- 24 y ^ { 3 } z + 12 y ^ { 2 } z + 8 y z ^ { 2 } + 4 y z ^ { 3 }$ 
D)  $- 24 y ^ { 3 } z + 12 y ^ { 3 } z ^ { 2 } + 8 y ^ { 2 } z ^ { 3 } - 4 y z ^ { 3 }$ 
E)  $- 24 y ^ { 3 } z + 20 y ^ { 2 } z ^ { 2 } - 8 y z ^ { 3 }$ 
A)  $- 24 y ^ { 3 } z + 20 y ^ { 2 } z ^ { 2 } + 4 y z ^ { 3 }$ 
B)  $- 24 y ^ { 3 } z + 20 y ^ { 2 } z ^ { 2 } - 4 y z ^ { 3 }$ 
C)  $- 24 y ^ { 3 } z + 12 y ^ { 2 } z + 8 y z ^ { 2 } + 4 y z ^ { 3 }$ 
D)  $- 24 y ^ { 3 } z + 12 y ^ { 3 } z ^ { 2 } + 8 y ^ { 2 } z ^ { 3 } - 4 y z ^ { 3 }$ 
E)  $- 24 y ^ { 3 } z + 20 y ^ { 2 } z ^ { 2 } - 8 y z ^ { 3 }$

Question 17

Factor the expression completely. If the expression is prime, so indicate. $625 x ^ { 4 } - 256 y ^ { 4 }$

Accepted Answer

A)  $\left( 25 x ^ { 2 } + 16 y ^ { 2 } \right) ( 4 x + 5 y ) ( 4 x - 5 y )$ 
B)  $( 5 x - 4 y ) ^ { 2 } ( 5 x - 4 y ) ^ { 2 }$ 
C)  $\left( 25 x ^ { 2 } + 16 y ^ { 2 } \right) ( 5 x + 4 y ) ( 5 x - 4 y )$ 
D)  $\left( 25 x ^ { 2 } - 16 y ^ { 2 } \right) ( 5 x - 4 y ) ( 5 x + 4 y )$ 
E)  prime 
A)  $\left( 25 x ^ { 2 } + 16 y ^ { 2 } \right) ( 4 x + 5 y ) ( 4 x - 5 y )$ 
B)  $( 5 x - 4 y ) ^ { 2 } ( 5 x - 4 y ) ^ { 2 }$ 
C)  $\left( 25 x ^ { 2 } + 16 y ^ { 2 } \right) ( 5 x + 4 y ) ( 5 x - 4 y )$ 
D)  $\left( 25 x ^ { 2 } - 16 y ^ { 2 } \right) ( 5 x - 4 y ) ( 5 x + 4 y )$ 
E)  prime

Question 18

Evaluate: $\left( 1 - \left( 1 - 7 ^ { - 1 } \right) ^ { - 1 } \right) ^ { - 1 }$

Accepted Answer

The answer of Evaluate: \(\left( 1 - \left( 1 -...

Question 19

Let $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 4 x + 2$ For what value(s) of x is $f ( x ) = 2$ ?
 If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Let \(f ( x ) = x...

Question 20

Simplify the expression. $- \frac { 5 t ^ { - 9 } t ^ { - 2 } } { t ^ { - 11 } }$

Accepted Answer

A)  $- \frac { t } { 5 }$ 
B)  $- 5 t$ 
C)  $- \frac { 1 } { 5 }$ 
D)  $- \frac { 5 } { t }$ 
E)  -5 
A)  $- \frac { t } { 5 }$ 
B)  $- 5 t$ 
C)  $- \frac { 1 } { 5 }$ 
D)  $- \frac { 5 } { t }$ 
E)  -5

Write the number in standard notation. $3.3 \times 10 ^ { - 8 }$

Solve the equation. $2 x ^ { 2 } + 6 x = 0$ , x = __________ If there is more than one solution, separate your answers with commas.

Solve: $( x - 4 ) ( x + 3 ) = 8$

Simplify the expression. $\left( \frac { a } { b ^ { 2 } } \right) ^ { 3 }$

Perform the indicated operations. $\left( 4 x ^ { 2 } + 3 x - 3 \right) + \left( 4 x ^ { 2 } - 2 x - 2 \right) - \left( x ^ { 2 } + x + 6 \right)$

Factor the expression completely. If the expression is prime, so indicate. $- 13 m ^ { 2 } + m ^ { 4 } + 36$

The length of a rectangular ice-skating rink is 20 meters greater than twice its width. Find the width. $w$ =__________ m

Factor the expression completely. If the expression is prime, so indicate. $27 x ^ { 3 } y ^ { 4 } - 8 y$

Factor the expression completely. $27 x ^ { 3 } y ^ { 4 } - 8 y$ If the expression is prime, so indicate.

Perform the indicated operations. $( a - b ) ( a + b ) ( a - 6 b )$

In any factoring problem, always factor out any _________ factors first.

Factor: $- 24 x ^ { 2 } + 70 x y + 66 y ^ { 2 }$

If $f ( x ) = 2 x ^ { 2 } - 4 x - 7$ , find $f ( c + 5 )$ .

Simplify: $\left( 2 x ^ { - 3 } \right) ^ { - 4 }$

Write the numbers in scientific notation and perform the operations. Give the answer in scientific notation and in standard notation. $( 85,000,000,000 ) ( 4,700,000,000 )$

Find the product. $- 4 y z ( 3 y - z ) ( 2 y - z )$

Factor the expression completely. If the expression is prime, so indicate. $625 x ^ { 4 } - 256 y ^ { 4 }$

Evaluate: $\left( 1 - \left( 1 - 7 ^ { - 1 } \right) ^ { - 1 } \right) ^ { - 1 }$

Let $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 4 x + 2$ For what value(s) of x is $f ( x ) = 2$ ? If there is more than one solution, separate your answers with commas.

Simplify the expression. $- \frac { 5 t ^ { - 9 } t ^ { - 2 } } { t ^ { - 11 } }$

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 the number in standard notation. 3.3×10−83.3 \times 10 ^ { - 8 }3.3×10−8

Solve the equation. 2x2+6x=02 x ^ { 2 } + 6 x = 02x2+6x=0 , x = __________ If there is more than one solution, separate your answers with commas.

Solve: (x−4)(x+3)=8( x - 4 ) ( x + 3 ) = 8(x−4)(x+3)=8

Simplify the expression. (ab2)3\left( \frac { a } { b ^ { 2 } } \right) ^ { 3 }(b2a​)3

Perform the indicated operations. (4x2+3x−3)+(4x2−2x−2)−(x2+x+6)\left( 4 x ^ { 2 } + 3 x - 3 \right) + \left( 4 x ^ { 2 } - 2 x - 2 \right) - \left( x ^ { 2 } + x + 6 \right)(4x2+3x−3)+(4x2−2x−2)−(x2+x+6)

Factor the expression completely. If the expression is prime, so indicate. −13m2+m4+36- 13 m ^ { 2 } + m ^ { 4 } + 36−13m2+m4+36

The length of a rectangular ice-skating rink is 20 meters greater than twice its width. Find the width. www =__________ m

Factor the expression completely. If the expression is prime, so indicate. 27x3y4−8y27 x ^ { 3 } y ^ { 4 } - 8 y27x3y4−8y

Factor the expression completely. 27x3y4−8y27 x ^ { 3 } y ^ { 4 } - 8 y27x3y4−8y If the expression is prime, so indicate.

Perform the indicated operations. (a−b)(a+b)(a−6b)( a - b ) ( a + b ) ( a - 6 b )(a−b)(a+b)(a−6b)

In any factoring problem, always factor out any _________ factors first.

Factor: −24x2+70xy+66y2- 24 x ^ { 2 } + 70 x y + 66 y ^ { 2 }−24x2+70xy+66y2

If f(x)=2x2−4x−7f ( x ) = 2 x ^ { 2 } - 4 x - 7f(x)=2x2−4x−7 , find f(c+5)f ( c + 5 )f(c+5) .

Simplify: (2x−3)−4\left( 2 x ^ { - 3 } \right) ^ { - 4 }(2x−3)−4

Write the numbers in scientific notation and perform the operations. Give the answer in scientific notation and in standard notation. (85,000,000,000)(4,700,000,000)( 85,000,000,000 ) ( 4,700,000,000 )(85,000,000,000)(4,700,000,000)

Find the product. −4yz(3y−z)(2y−z)- 4 y z ( 3 y - z ) ( 2 y - z )−4yz(3y−z)(2y−z)

Factor the expression completely. If the expression is prime, so indicate. 625x4−256y4625 x ^ { 4 } - 256 y ^ { 4 }625x4−256y4

Evaluate: (1−(1−7−1)−1)−1\left( 1 - \left( 1 - 7 ^ { - 1 } \right) ^ { - 1 } \right) ^ { - 1 }(1−(1−7−1)−1)−1

Let f(x)=x3−5x2+4x+2f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 4 x + 2f(x)=x3−5x2+4x+2 For what value(s) of x is f(x)=2f ( x ) = 2f(x)=2 ? If there is more than one solution, separate your answers with commas.

Simplify the expression. −5t−9t−2t−11- \frac { 5 t ^ { - 9 } t ^ { - 2 } } { t ^ { - 11 } }−t−115t−9t−2​

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 the number in standard notation. $3.3 \times 10 ^ { - 8 }$

Solve the equation. $2 x ^ { 2 } + 6 x = 0$ , x = __________ If there is more than one solution, separate your answers with commas.

Solve: $( x - 4 ) ( x + 3 ) = 8$

Simplify the expression. $\left( \frac { a } { b ^ { 2 } } \right) ^ { 3 }$

Perform the indicated operations. $\left( 4 x ^ { 2 } + 3 x - 3 \right) + \left( 4 x ^ { 2 } - 2 x - 2 \right) - \left( x ^ { 2 } + x + 6 \right)$

Factor the expression completely. If the expression is prime, so indicate. $- 13 m ^ { 2 } + m ^ { 4 } + 36$

The length of a rectangular ice-skating rink is 20 meters greater than twice its width. Find the width. $w$ =__________ m

Factor the expression completely. If the expression is prime, so indicate. $27 x ^ { 3 } y ^ { 4 } - 8 y$

Factor the expression completely. $27 x ^ { 3 } y ^ { 4 } - 8 y$ If the expression is prime, so indicate.

Perform the indicated operations. $( a - b ) ( a + b ) ( a - 6 b )$

Factor: $- 24 x ^ { 2 } + 70 x y + 66 y ^ { 2 }$

If $f ( x ) = 2 x ^ { 2 } - 4 x - 7$ , find $f ( c + 5 )$ .

Simplify: $\left( 2 x ^ { - 3 } \right) ^ { - 4 }$

Write the numbers in scientific notation and perform the operations. Give the answer in scientific notation and in standard notation. $( 85,000,000,000 ) ( 4,700,000,000 )$

Find the product. $- 4 y z ( 3 y - z ) ( 2 y - z )$

Factor the expression completely. If the expression is prime, so indicate. $625 x ^ { 4 } - 256 y ^ { 4 }$

Evaluate: $\left( 1 - \left( 1 - 7 ^ { - 1 } \right) ^ { - 1 } \right) ^ { - 1 }$

Let $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 4 x + 2$ For what value(s) of x is $f ( x ) = 2$ ? If there is more than one solution, separate your answers with commas.

Simplify the expression. $- \frac { 5 t ^ { - 9 } t ^ { - 2 } } { t ^ { - 11 } }$