Question 1

Factor the expression completely. If the expression is prime, so indicate. $5 a ^ { 2 } b c + 5 a b c - 100 b c$

Accepted Answer

A)  $5 b c ( a + 4 ) ( a - 5 )$ 
B)  $5 b c ( a + 4 ) ( a + 5 )$ 
C)  $5 b c ( a - 4 ) ( a + 5 )$ 
D)  $5 b c ( a - 5 ) ( a + 6 )$ 
E)  prime 
A)  $5 b c ( a + 4 ) ( a - 5 )$ 
B)  $5 b c ( a + 4 ) ( a + 5 )$ 
C)  $5 b c ( a - 4 ) ( a + 5 )$ 
D)  $5 b c ( a - 5 ) ( a + 6 )$ 
E)  prime

Question 2

$x ^ { 2 } - y ^ { 2 }$ is called a _________ of two squares.

Accepted Answer

The answer of \(x ^ { 2 } - y...

Question 3

Write the number in scientific notation. $323 \times 10 ^ { 5 }$

Accepted Answer

A)  $0.323 \times 10 ^ { 8 }$ 
B)  $32.3 \times 10 ^ { 8 }$ 
C)  $3.23 \times 10 ^ { 7 }$ 
D)  $3.23 \times 10 ^ { 8 }$ 
E)  $3.23 \times 10 ^ { 3 }$ 
A)  $0.323 \times 10 ^ { 8 }$ 
B)  $32.3 \times 10 ^ { 8 }$ 
C)  $3.23 \times 10 ^ { 7 }$ 
D)  $3.23 \times 10 ^ { 8 }$ 
E)  $3.23 \times 10 ^ { 3 }$

Question 4

Perform the indicated operation: $- 3 x ^ { 4 } y \left( 5 x ^ { 3 } y ^ { 2 } - 7 x \right)$

Accepted Answer

A)  $- 15 x ^ { 7 } y ^ { 3 } + 21 x ^ { 5 } y$ 
B)  $- 15 x ^ { 7 } y ^ { 3 } - 21 x ^ { 5 } y$ 
C)  $6 x ^ { 6 } y ^ { 3 }$ 
D)  $- 15 x ^ { 12 } y ^ { 2 } + 21 x ^ { 4 } y$ 
A)  $- 15 x ^ { 7 } y ^ { 3 } + 21 x ^ { 5 } y$ 
B)  $- 15 x ^ { 7 } y ^ { 3 } - 21 x ^ { 5 } y$ 
C)  $6 x ^ { 6 } y ^ { 3 }$ 
D)  $- 15 x ^ { 12 } y ^ { 2 } + 21 x ^ { 4 } y$

Question 5

Multiply: $( 5 x - 2 ) ^ { 3 }$

Accepted Answer

A)  $125 x ^ { 3 } - 50 x ^ { 2 } + 20 x - 8$ 
B)  $125 x ^ { 3 } - 100 x ^ { 2 } + 40 x - 8$ 
C)  $125 x ^ { 3 } - 150 x ^ { 2 } + 300 x - 20$ 
D)  $125 x ^ { 3 } - 150 x ^ { 2 } + 60 x - 8$ 
A)  $125 x ^ { 3 } - 50 x ^ { 2 } + 20 x - 8$ 
B)  $125 x ^ { 3 } - 100 x ^ { 2 } + 40 x - 8$ 
C)  $125 x ^ { 3 } - 150 x ^ { 2 } + 300 x - 20$ 
D)  $125 x ^ { 3 } - 150 x ^ { 2 } + 60 x - 8$

Question 6

Solve the equation. $x ^ { 3 } - 7 x ^ { 2 } = 8 x$

Accepted Answer

A)  $x = 0 , x = 10 , x = - 8$ 
B)  $x = 0 , x = - 1 , x = 8$ 
C)  $x = 9 , x = - 12 , x = 10$ 
D)  $x = 9 , x = - 1 , x = 8$ 
E)  $x = 0 , x = - 1 , x = 11$ 
A)  $x = 0 , x = 10 , x = - 8$ 
B)  $x = 0 , x = - 1 , x = 8$ 
C)  $x = 9 , x = - 12 , x = 10$ 
D)  $x = 9 , x = - 1 , x = 8$ 
E)  $x = 0 , x = - 1 , x = 11$

Question 7

Solve: $25 x ^ { 2 } - 5 x - 12 = 0$

Accepted Answer

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

Question 8

Simplify: $\frac { a ^ { - 2 } } { a ^ { - 14 } }$

Accepted Answer

A)  $a ^ { 7 }$ 
B)  $\frac { 1 } { a ^ { 16 } }$ 
C)  $\frac { 1 } { a ^ { 12 } }$ 
D)  $a ^ { 12 }$ 
A)  $a ^ { 7 }$ 
B)  $\frac { 1 } { a ^ { 16 } }$ 
C)  $\frac { 1 } { a ^ { 12 } }$ 
D)  $a ^ { 12 }$

Question 9

Explain why $123.5 \times 10 ^ { 5 }$ is not written in scientific notation.

Accepted Answer

A positive number is written i

Question 10

Factor the expression completely. If the expression is prime, so indicate. $x y - 4 t y + x s ^ { 2 } - 4 t s ^ { 2 }$

Accepted Answer

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

Question 11

The cost for a guitar maker to handcraft x guitars is given by the function $C ( x )$ . The revenue taken in with the sales of x guitars is given by the function $R ( x )$ . Find the number of guitars that must be sold so that the cost equals the revenue. $C ( x ) = \frac { 1 } { 8 } x ^ { 2 } - x + 30$ $R ( x ) = \frac { 1 } { 4 } x ^ { 2 }$ __________ guitars

Accepted Answer

The answer of The cost for a guitar maker to...

Question 12

Use a special product formula to find the product. $( a - 8 b ) ^ { 2 }$

Accepted Answer

The answer of Use a special product formula to find...

Question 13

Multiply. $( 7 t - 6 ) ( 2 t + 3 )$

Accepted Answer

The answer of Multiply. \(( 7 t - 6 )...

Question 14

Solve the equation. $- z ^ { 4 } + 26 z ^ { 2 } - 25 = 0$

Accepted Answer

A)  $z = 1 , z = - 1 , z = 4 , z = - 4$ 
B)  $z = 1 , z = 5$ 
C)  $z = 1 , z = 25$ 
D)  $z = 1 , z = - 1 , z = 2 , z = - 2$ 
E)  $z = 1 , z = - 1 , z = 5 , z = - 5$ 
A)  $z = 1 , z = - 1 , z = 4 , z = - 4$ 
B)  $z = 1 , z = 5$ 
C)  $z = 1 , z = 25$ 
D)  $z = 1 , z = - 1 , z = 2 , z = - 2$ 
E)  $z = 1 , z = - 1 , z = 5 , z = - 5$

Question 15

What polynomial should be subtracted from $2 x ^ { 3 } y ^ { 3 } - 6 x y + 3 y$ to obtain the polynomial $- 4 x ^ { 3 } y ^ { 3 } - 13 x y + 13 y$ ?

Accepted Answer

The answer of What polynomial should be subtracted from \(2...

Question 16

Simplify the polynomial. $9 x ^ { 2 } + 4 x - 3 x - 3 + 5 x ^ { 2 }$

Accepted Answer

A)  $4 x ^ { 2 } + 4 x + 3$ 
B)  $14 x ^ { 2 } - x + 3$ 
C)  $14 x ^ { 2 } + 7 x - 3$ 
D)  $14 x ^ { 2 } + x - 3$ 
E)  $4 x ^ { 2 } + 3 x - 3$ 
A)  $4 x ^ { 2 } + 4 x + 3$ 
B)  $14 x ^ { 2 } - x + 3$ 
C)  $14 x ^ { 2 } + 7 x - 3$ 
D)  $14 x ^ { 2 } + x - 3$ 
E)  $4 x ^ { 2 } + 3 x - 3$

Question 17

Classify the polynomial as a monomial, binomial, trinomial, or none of these. $5 x ^ { 8 } + 6 y ^ { 4 }$

Accepted Answer

A)  monomial 
B)  binomial 
C)  trinomial 
D)  none of these 
A)  monomial 
B)  binomial 
C)  trinomial 
D)  none of these

Question 18

Simplify the expression. $\left( \frac { 3 a ^ { 3 } b } { a ^ { - 2 } b ^ { 4 } } \right) ^ { 3 }$

Accepted Answer

A)  $\frac { 27 a ^ { 15 } } { b ^ { 9 } }$ 
B)  $\frac { 27 a ^ { 3 } } { b ^ { 9 } }$ 
C)  $\frac { 27 } { a ^ { 3 } b ^ { 9 } }$ 
D)  $\frac { 27 b ^ { 9 } } { a ^ { 15 } }$ 
E)  $27 a ^ { 15 } b ^ { 9 }$ 
A)  $\frac { 27 a ^ { 15 } } { b ^ { 9 } }$ 
B)  $\frac { 27 a ^ { 3 } } { b ^ { 9 } }$ 
C)  $\frac { 27 } { a ^ { 3 } b ^ { 9 } }$ 
D)  $\frac { 27 b ^ { 9 } } { a ^ { 15 } }$ 
E)  $27 a ^ { 15 } b ^ { 9 }$

Question 19

Write the numbers in scientific notation and perform the operations. $\frac { 0.00000184 } { 0.0004 }$ Give the answer in scientific notation and in standard notation.

Accepted Answer

A)  $4.6 \times 10 ^ { - 4 } , 0.00046$ 
B)  $0.46 \times 10 ^ { - 3 } , 0.00046$ 
C)  $0.46 \times 10 ^ { - 2 } , 0.0046$ 
D)  $4.6 \times 10 ^ { - 2 } , 0.046$ 
E)  $4.6 \times 10 ^ { - 3 } , 0.0046$ 
A)  $4.6 \times 10 ^ { - 4 } , 0.00046$ 
B)  $0.46 \times 10 ^ { - 3 } , 0.00046$ 
C)  $0.46 \times 10 ^ { - 2 } , 0.0046$ 
D)  $4.6 \times 10 ^ { - 2 } , 0.046$ 
E)  $4.6 \times 10 ^ { - 3 } , 0.0046$

Question 20

Simplify the polynomial. $12 x ^ { 2 } + 2 x - 1 x - 3 + 5 x ^ { 2 }$

Accepted Answer

The answer of Simplify the polynomial. \(12 x ^ {...

Factor the expression completely. If the expression is prime, so indicate. $5 a ^ { 2 } b c + 5 a b c - 100 b c$

$x ^ { 2 } - y ^ { 2 }$ is called a _________ of two squares.

Write the number in scientific notation. $323 \times 10 ^ { 5 }$

Perform the indicated operation: $- 3 x ^ { 4 } y \left( 5 x ^ { 3 } y ^ { 2 } - 7 x \right)$

Multiply: $( 5 x - 2 ) ^ { 3 }$

Solve the equation. $x ^ { 3 } - 7 x ^ { 2 } = 8 x$

Solve: $25 x ^ { 2 } - 5 x - 12 = 0$

Simplify: $\frac { a ^ { - 2 } } { a ^ { - 14 } }$

Explain why $123.5 \times 10 ^ { 5 }$ is not written in scientific notation.

Factor the expression completely. If the expression is prime, so indicate. $x y - 4 t y + x s ^ { 2 } - 4 t s ^ { 2 }$

Use a special product formula to find the product. $( a - 8 b ) ^ { 2 }$

Multiply. $( 7 t - 6 ) ( 2 t + 3 )$

Solve the equation. $- z ^ { 4 } + 26 z ^ { 2 } - 25 = 0$

What polynomial should be subtracted from $2 x ^ { 3 } y ^ { 3 } - 6 x y + 3 y$ to obtain the polynomial $- 4 x ^ { 3 } y ^ { 3 } - 13 x y + 13 y$ ?

Simplify the polynomial. $9 x ^ { 2 } + 4 x - 3 x - 3 + 5 x ^ { 2 }$

Classify the polynomial as a monomial, binomial, trinomial, or none of these. $5 x ^ { 8 } + 6 y ^ { 4 }$

Simplify the expression. $\left( \frac { 3 a ^ { 3 } b } { a ^ { - 2 } b ^ { 4 } } \right) ^ { 3 }$

Write the numbers in scientific notation and perform the operations. $\frac { 0.00000184 } { 0.0004 }$ Give the answer in scientific notation and in standard notation.

Simplify the polynomial. $12 x ^ { 2 } + 2 x - 1 x - 3 + 5 x ^ { 2 }$

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

Exam 5: Exponents, Polynomials, and Polynomial Functions

Factor the expression completely. If the expression is prime, so indicate. 5a2bc+5abc−100bc5 a ^ { 2 } b c + 5 a b c - 100 b c5a2bc+5abc−100bc

x2−y2x ^ { 2 } - y ^ { 2 }x2−y2 is called a _________ of two squares.

Write the number in scientific notation. 323×105323 \times 10 ^ { 5 }323×105

Perform the indicated operation: −3x4y(5x3y2−7x)- 3 x ^ { 4 } y \left( 5 x ^ { 3 } y ^ { 2 } - 7 x \right)−3x4y(5x3y2−7x)

Multiply: (5x−2)3( 5 x - 2 ) ^ { 3 }(5x−2)3

Solve the equation. x3−7x2=8xx ^ { 3 } - 7 x ^ { 2 } = 8 xx3−7x2=8x

Solve: 25x2−5x−12=025 x ^ { 2 } - 5 x - 12 = 025x2−5x−12=0

Simplify: a−2a−14\frac { a ^ { - 2 } } { a ^ { - 14 } }a−14a−2​

Explain why 123.5×105123.5 \times 10 ^ { 5 }123.5×105 is not written in scientific notation.

Factor the expression completely. If the expression is prime, so indicate. xy−4ty+xs2−4ts2x y - 4 t y + x s ^ { 2 } - 4 t s ^ { 2 }xy−4ty+xs2−4ts2

Use a special product formula to find the product. (a−8b)2( a - 8 b ) ^ { 2 }(a−8b)2

Multiply. (7t−6)(2t+3)( 7 t - 6 ) ( 2 t + 3 )(7t−6)(2t+3)

Solve the equation. −z4+26z2−25=0- z ^ { 4 } + 26 z ^ { 2 } - 25 = 0−z4+26z2−25=0

What polynomial should be subtracted from 2x3y3−6xy+3y2 x ^ { 3 } y ^ { 3 } - 6 x y + 3 y2x3y3−6xy+3y to obtain the polynomial −4x3y3−13xy+13y- 4 x ^ { 3 } y ^ { 3 } - 13 x y + 13 y−4x3y3−13xy+13y ?

Simplify the polynomial. 9x2+4x−3x−3+5x29 x ^ { 2 } + 4 x - 3 x - 3 + 5 x ^ { 2 }9x2+4x−3x−3+5x2

Classify the polynomial as a monomial, binomial, trinomial, or none of these. 5x8+6y45 x ^ { 8 } + 6 y ^ { 4 }5x8+6y4

Simplify the expression. (3a3ba−2b4)3\left( \frac { 3 a ^ { 3 } b } { a ^ { - 2 } b ^ { 4 } } \right) ^ { 3 }(a−2b43a3b​)3

Write the numbers in scientific notation and perform the operations. 0.000001840.0004\frac { 0.00000184 } { 0.0004 }0.00040.00000184​ Give the answer in scientific notation and in standard notation.

Simplify the polynomial. 12x2+2x−1x−3+5x212 x ^ { 2 } + 2 x - 1 x - 3 + 5 x ^ { 2 }12x2+2x−1x−3+5x2

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

Factor the expression completely. If the expression is prime, so indicate. $5 a ^ { 2 } b c + 5 a b c - 100 b c$

$x ^ { 2 } - y ^ { 2 }$ is called a _________ of two squares.

Write the number in scientific notation. $323 \times 10 ^ { 5 }$

Perform the indicated operation: $- 3 x ^ { 4 } y \left( 5 x ^ { 3 } y ^ { 2 } - 7 x \right)$

Multiply: $( 5 x - 2 ) ^ { 3 }$

Solve the equation. $x ^ { 3 } - 7 x ^ { 2 } = 8 x$

Solve: $25 x ^ { 2 } - 5 x - 12 = 0$

Simplify: $\frac { a ^ { - 2 } } { a ^ { - 14 } }$

Explain why $123.5 \times 10 ^ { 5 }$ is not written in scientific notation.

Factor the expression completely. If the expression is prime, so indicate. $x y - 4 t y + x s ^ { 2 } - 4 t s ^ { 2 }$

Use a special product formula to find the product. $( a - 8 b ) ^ { 2 }$

Multiply. $( 7 t - 6 ) ( 2 t + 3 )$

Solve the equation. $- z ^ { 4 } + 26 z ^ { 2 } - 25 = 0$

What polynomial should be subtracted from $2 x ^ { 3 } y ^ { 3 } - 6 x y + 3 y$ to obtain the polynomial $- 4 x ^ { 3 } y ^ { 3 } - 13 x y + 13 y$ ?

Simplify the polynomial. $9 x ^ { 2 } + 4 x - 3 x - 3 + 5 x ^ { 2 }$

Classify the polynomial as a monomial, binomial, trinomial, or none of these. $5 x ^ { 8 } + 6 y ^ { 4 }$

Simplify the expression. $\left( \frac { 3 a ^ { 3 } b } { a ^ { - 2 } b ^ { 4 } } \right) ^ { 3 }$

Write the numbers in scientific notation and perform the operations. $\frac { 0.00000184 } { 0.0004 }$ Give the answer in scientific notation and in standard notation.

Simplify the polynomial. $12 x ^ { 2 } + 2 x - 1 x - 3 + 5 x ^ { 2 }$