Question 1

Use synthetic division to perform the division. $\frac { 3 x ^ { 3 } - 13 x ^ { 2 } + 7 x - 12 } { x - 4 }$

Accepted Answer

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

Question 2

Solve the problem by writing a variation model. The number of days that a given number of bushels of corn will last when feeding cattle varies inversely as the number of animals. If x bushels will feed 27 cows for 10 days, how long will the feed last for 10 cows?

Accepted Answer

A)  29 days 
B)  31 days 
C)  27 days 
D)  28 days 
E)  30 days 
A)  29 days 
B)  31 days 
C)  27 days 
D)  28 days 
E)  30 days

Question 3

Simplify: $\left( \frac { 3 x + 1 } { 12 x ^ { 3 } - 27 x ^ { 2 } + 6 x } \right) \div \left( \frac { 1 } { 4 x - 1 } + \frac { 1 } { 2 - x } \right)$

Accepted Answer

The answer of Simplify: \(\left( \frac { 3 x +...

Question 4

If two angles of one triangle have the same measure as two angles of a second triangle, the triangles are _________.

Accepted Answer

The answer of If two angles of one triangle have...

Question 5

Perform the division. $2 x ^ { 2 } - 5 x + 5$

Accepted Answer

A)  $3 x + 4 - \frac { 12 x - 23 } { 2 x ^ { 2 } - 5 x + 5 }$ 
B)  $3 x + 4 - \frac { 12 x + 23 } { 2 x ^ { 2 } - 5 x + 5 }$ 
C)  $3 x + 4 + \frac { 12 x - 23 } { 2 x ^ { 2 } - 5 x + 5 }$ 
D)  $3 x - 4 + \frac { 12 x - 23 } { 2 x ^ { 2 } - 5 x + 5 }$ 
E)  $3 x + 4 + \frac { 12 x + 23 } { 2 x ^ { 2 } - 5 x + 5 }$ 
A)  $3 x + 4 - \frac { 12 x - 23 } { 2 x ^ { 2 } - 5 x + 5 }$ 
B)  $3 x + 4 - \frac { 12 x + 23 } { 2 x ^ { 2 } - 5 x + 5 }$ 
C)  $3 x + 4 + \frac { 12 x - 23 } { 2 x ^ { 2 } - 5 x + 5 }$ 
D)  $3 x - 4 + \frac { 12 x - 23 } { 2 x ^ { 2 } - 5 x + 5 }$ 
E)  $3 x + 4 + \frac { 12 x + 23 } { 2 x ^ { 2 } - 5 x + 5 }$

Question 6

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = 3 x ^ { 3 } + x + 3 ; k = 1$ $P ( 1 ) =$ __________

Accepted Answer

The answer of Use the remainder theorem and synthetic division...

Question 7

Solve: $\frac { 1 } { f } = \frac { 1 } { s _ { 1 } } + \frac { 1 } { s _ { 2 } }$ for $f$

Accepted Answer

A)  $f = \frac { s _ { 1 } s _ { 2 } } { s _ { 1 } + s _ { 2 } }$ 
B)  $f = + 1$ 
C)  $f = s _ { 1 } + s _ { 2 }$ 
D)  $f = \frac { s _ { 1 } s _ { 2 } } { s _ { 1 } - s _ { 2 } }$ 
A)  $f = \frac { s _ { 1 } s _ { 2 } } { s _ { 1 } + s _ { 2 } }$ 
B)  $f = + 1$ 
C)  $f = s _ { 1 } + s _ { 2 }$ 
D)  $f = \frac { s _ { 1 } s _ { 2 } } { s _ { 1 } - s _ { 2 } }$

Question 8

Which of the following is a factor of $P ( x ) = 3 x ^ { 3 } + 8 x ^ { 2 } - 9 x - 18$ ?

Accepted Answer

A)  $x - 3$ 
B)  $x - 2$ 
C)  $x + 2$ 
D)  $x + 3$ 
A)  $x - 3$ 
B)  $x - 2$ 
C)  $x + 2$ 
D)  $x + 3$

Question 9

Use synthetic division to perform the division. $\left( x ^ { 2 } - 3 x + 28 \right) \div ( x + 4 )$

Accepted Answer

A)  $x + 7 + \frac { 56 } { x + 4 }$ 
B)  $x - 7$ 
C)  $x - 7 + \frac { 56 } { x + 4 }$ 
D)  $x - 7 + \frac { 56 } { x - 4 }$ 
E)  $x - 4 + \frac { 56 } { x + 7 }$ 
A)  $x + 7 + \frac { 56 } { x + 4 }$ 
B)  $x - 7$ 
C)  $x - 7 + \frac { 56 } { x + 4 }$ 
D)  $x - 7 + \frac { 56 } { x - 4 }$ 
E)  $x - 4 + \frac { 56 } { x + 7 }$

Question 10

Perform the indicated operation. Simplify, if possible. $\frac { 8 x ^ { 2 } + 2 x - 3 } { 8 x ^ { 2 } - 2 } \div \frac { 12 x + 9 } { 16 x ^ { 2 } + 12 x + 2 }$

Accepted Answer

A)  $\frac { 3 ( 4 x + 3 ) ^ { 2 } } { 4 ( 2 x + 1 ) ^ { 2 } ( 4 x + 1 ) }$ 
B)  $\frac { 4 x + 1 } { 3 }$ 
C)  $\frac { ( 4 x - 3 ) ( 2 x + 1 ) ( 4 x + 1 ) } { 3 ( 2 x - 1 ) ( 4 x + 3 ) }$ 
D)  $\frac { ( 4 x - 3 ) ( 4 x - 1 ) } { 3 ( 4 x + 3 ) }$ 
A)  $\frac { 3 ( 4 x + 3 ) ^ { 2 } } { 4 ( 2 x + 1 ) ^ { 2 } ( 4 x + 1 ) }$ 
B)  $\frac { 4 x + 1 } { 3 }$ 
C)  $\frac { ( 4 x - 3 ) ( 2 x + 1 ) ( 4 x + 1 ) } { 3 ( 2 x - 1 ) ( 4 x + 3 ) }$ 
D)  $\frac { ( 4 x - 3 ) ( 4 x - 1 ) } { 3 ( 4 x + 3 ) }$

Question 11

Perform the operations and simplify the result when possible. $\frac { 8 x } { x + 1 } + \frac { 5 } { x + 1 } - \frac { 3 x } { x + 1 }$

Accepted Answer

A)  9 
B)  5 x 
C)  8 x 
D)  7 
E)  5 
A)  9 
B)  5 x 
C)  8 x 
D)  7 
E)  5

Question 12

Perform the indicated operation. Simplify, if possible. $\frac { 5 x + 1 } { x ^ { 2 } - 5 x - 14 } - \frac { x - 7 } { x ^ { 2 } - 5 x - 14 }$

Accepted Answer

A)  $\frac { 4 x ^ { 2 } - 6 } { ( x - 7 ) ( x + 2 ) }$ 
B)  $\frac { 4 x + 8 } { ( x - 7 ) ( x + 2 ) }$ 
C)  $\frac { 4 x ^ { 2 } + 8 } { ( x - 7 ) ( x + 2 ) }$ 
D)  $\frac { 4 } { x - 7 }$ 
A)  $\frac { 4 x ^ { 2 } - 6 } { ( x - 7 ) ( x + 2 ) }$ 
B)  $\frac { 4 x + 8 } { ( x - 7 ) ( x + 2 ) }$ 
C)  $\frac { 4 x ^ { 2 } + 8 } { ( x - 7 ) ( x + 2 ) }$ 
D)  $\frac { 4 } { x - 7 }$

Question 13

Perform the operations and simplify the result when possible. $\frac { 2 } { a b ^ { 2 } } - \frac { 3 } { a ^ { 2 } b }$

Accepted Answer

The answer of Perform the operations and simplify the result...

Question 14

Solve the formula for the indicated variable. $\frac { 1 } { q } + \frac { 1 } { p } = 1$ for q

Accepted Answer

The answer of Solve the formula for the indicated variable....

Question 15

Fill in the blank with the appropriate phrase. The least __________ of $\frac { x - 8 } { x + 4 }$ and $\frac { 4 - 5 x } { x }$ is $x ( x + 4 )$ .

Accepted Answer

The answer of Fill in the blank with the appropriate...

Question 16

A woman can bicycle 28 miles in the same time as it takes her to walk 6 miles. She can ride 11 mph faster than she can walk. How fast can she walk?

Accepted Answer

The answer of A woman can bicycle 28 miles in...

Question 17

Solve: $A = \frac { D } { B + C }$ for D .

Accepted Answer

A)  $\frac { A } { B + C }$ 
B)  $A ( B + C )$ 
C)  $A B + C$ 
D)  $\frac { B + C } { A }$ 
A)  $\frac { A } { B + C }$ 
B)  $A ( B + C )$ 
C)  $A B + C$ 
D)  $\frac { B + C } { A }$

Question 18

On average, it takes a teacher 45 minutes to grade a set of quizzes. It takes her teacher's aide twice as long to do the same grading. How long will it take if they work together to grade a set of quizzes?
 __________ min

Accepted Answer

The answer of On average, it takes a teacher 45...

Question 19

To multiply rational expressions, multiply their numerators and multiply their _________.

Accepted Answer

The answer of To multiply rational expressions, multiply their numerators...

Question 20

Solve the equation and check the result. If the equation has no solution, answer none . $\frac { 1 } { 18 } + \frac { 1 } { n } - \frac { 2 } { 27 } = 0$  n= __________ Find the extraneous solution. $n \neq$ __________

Accepted Answer

The answer of Solve the equation and check the result....

Use synthetic division to perform the division. $\frac { 3 x ^ { 3 } - 13 x ^ { 2 } + 7 x - 12 } { x - 4 }$

Solve the problem by writing a variation model. The number of days that a given number of bushels of corn will last when feeding cattle varies inversely as the number of animals. If x bushels will feed 27 cows for 10 days, how long will the feed last for 10 cows?

Simplify: $\left( \frac { 3 x + 1 } { 12 x ^ { 3 } - 27 x ^ { 2 } + 6 x } \right) \div \left( \frac { 1 } { 4 x - 1 } + \frac { 1 } { 2 - x } \right)$

If two angles of one triangle have the same measure as two angles of a second triangle, the triangles are _________.

Perform the division. $2 x ^ { 2 } - 5 x + 5$ $Perform the division. 2 x ^ { 2 } - 5 x + 5$

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = 3 x ^ { 3 } + x + 3 ; k = 1$ $P ( 1 ) =$ __________

Solve: $\frac { 1 } { f } = \frac { 1 } { s _ { 1 } } + \frac { 1 } { s _ { 2 } }$ for $f$

Which of the following is a factor of $P ( x ) = 3 x ^ { 3 } + 8 x ^ { 2 } - 9 x - 18$ ?

Use synthetic division to perform the division. $\left( x ^ { 2 } - 3 x + 28 \right) \div ( x + 4 )$

Perform the indicated operation. Simplify, if possible. $\frac { 8 x ^ { 2 } + 2 x - 3 } { 8 x ^ { 2 } - 2 } \div \frac { 12 x + 9 } { 16 x ^ { 2 } + 12 x + 2 }$

Perform the operations and simplify the result when possible. $\frac { 8 x } { x + 1 } + \frac { 5 } { x + 1 } - \frac { 3 x } { x + 1 }$

Perform the indicated operation. Simplify, if possible. $\frac { 5 x + 1 } { x ^ { 2 } - 5 x - 14 } - \frac { x - 7 } { x ^ { 2 } - 5 x - 14 }$

Perform the operations and simplify the result when possible. $\frac { 2 } { a b ^ { 2 } } - \frac { 3 } { a ^ { 2 } b }$

Solve the formula for the indicated variable. $\frac { 1 } { q } + \frac { 1 } { p } = 1$ for q

Fill in the blank with the appropriate phrase. The least __________ of $\frac { x - 8 } { x + 4 }$ and $\frac { 4 - 5 x } { x }$ is $x ( x + 4 )$ .

A woman can bicycle 28 miles in the same time as it takes her to walk 6 miles. She can ride 11 mph faster than she can walk. How fast can she walk?

Solve: $A = \frac { D } { B + C }$ for D .

On average, it takes a teacher 45 minutes to grade a set of quizzes. It takes her teacher's aide twice as long to do the same grading. How long will it take if they work together to grade a set of quizzes? __________ min

To multiply rational expressions, multiply their numerators and multiply their _________.

Solve the equation and check the result. If the equation has no solution, answer none . $\frac { 1 } { 18 } + \frac { 1 } { n } - \frac { 2 } { 27 } = 0$ n= Find the extraneous solution. $n \neq$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 6: Rational Expression and Equations

Use synthetic division to perform the division. 3x3−13x2+7x−12x−4\frac { 3 x ^ { 3 } - 13 x ^ { 2 } + 7 x - 12 } { x - 4 }x−43x3−13x2+7x−12​

Solve the problem by writing a variation model. The number of days that a given number of bushels of corn will last when feeding cattle varies inversely as the number of animals. If x bushels will feed 27 cows for 10 days, how long will the feed last for 10 cows?

Simplify: (3x+112x3−27x2+6x)÷(14x−1+12−x)\left( \frac { 3 x + 1 } { 12 x ^ { 3 } - 27 x ^ { 2 } + 6 x } \right) \div \left( \frac { 1 } { 4 x - 1 } + \frac { 1 } { 2 - x } \right)(12x3−27x2+6x3x+1​)÷(4x−11​+2−x1​)

If two angles of one triangle have the same measure as two angles of a second triangle, the triangles are _________.

Perform the division. 2x2−5x+52 x ^ { 2 } - 5 x + 52x2−5x+5

Use the remainder theorem and synthetic division to find P ( k ). P(x)=3x3+x+3;k=1P ( x ) = 3 x ^ { 3 } + x + 3 ; k = 1P(x)=3x3+x+3;k=1 P(1)=P ( 1 ) =P(1)= __________

Solve: 1f=1s1+1s2\frac { 1 } { f } = \frac { 1 } { s _ { 1 } } + \frac { 1 } { s _ { 2 } }f1​=s1​1​+s2​1​ for fff

Which of the following is a factor of P(x)=3x3+8x2−9x−18P ( x ) = 3 x ^ { 3 } + 8 x ^ { 2 } - 9 x - 18P(x)=3x3+8x2−9x−18 ?

Use synthetic division to perform the division. (x2−3x+28)÷(x+4)\left( x ^ { 2 } - 3 x + 28 \right) \div ( x + 4 )(x2−3x+28)÷(x+4)

Perform the indicated operation. Simplify, if possible. 8x2+2x−38x2−2÷12x+916x2+12x+2\frac { 8 x ^ { 2 } + 2 x - 3 } { 8 x ^ { 2 } - 2 } \div \frac { 12 x + 9 } { 16 x ^ { 2 } + 12 x + 2 }8x2−28x2+2x−3​÷16x2+12x+212x+9​

Perform the operations and simplify the result when possible. 8xx+1+5x+1−3xx+1\frac { 8 x } { x + 1 } + \frac { 5 } { x + 1 } - \frac { 3 x } { x + 1 }x+18x​+x+15​−x+13x​

Perform the indicated operation. Simplify, if possible. 5x+1x2−5x−14−x−7x2−5x−14\frac { 5 x + 1 } { x ^ { 2 } - 5 x - 14 } - \frac { x - 7 } { x ^ { 2 } - 5 x - 14 }x2−5x−145x+1​−x2−5x−14x−7​

Perform the operations and simplify the result when possible. 2ab2−3a2b\frac { 2 } { a b ^ { 2 } } - \frac { 3 } { a ^ { 2 } b }ab22​−a2b3​

Solve the formula for the indicated variable. 1q+1p=1\frac { 1 } { q } + \frac { 1 } { p } = 1q1​+p1​=1 for q

Fill in the blank with the appropriate phrase. The least __________ of x−8x+4\frac { x - 8 } { x + 4 }x+4x−8​ and 4−5xx\frac { 4 - 5 x } { x }x4−5x​ is x(x+4)x ( x + 4 )x(x+4) .

A woman can bicycle 28 miles in the same time as it takes her to walk 6 miles. She can ride 11 mph faster than she can walk. How fast can she walk?

Solve: A=DB+CA = \frac { D } { B + C }A=B+CD​ for D .

On average, it takes a teacher 45 minutes to grade a set of quizzes. It takes her teacher's aide twice as long to do the same grading. How long will it take if they work together to grade a set of quizzes? __________ min

To multiply rational expressions, multiply their numerators and multiply their _________.

Solve the equation and check the result. If the equation has no solution, answer none . 118+1n−227=0\frac { 1 } { 18 } + \frac { 1 } { n } - \frac { 2 } { 27 } = 0181​+n1​−272​=0 n= __________ Find the extraneous solution. n≠n \neqn= __________

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Use synthetic division to perform the division. $\frac { 3 x ^ { 3 } - 13 x ^ { 2 } + 7 x - 12 } { x - 4 }$

Simplify: $\left( \frac { 3 x + 1 } { 12 x ^ { 3 } - 27 x ^ { 2 } + 6 x } \right) \div \left( \frac { 1 } { 4 x - 1 } + \frac { 1 } { 2 - x } \right)$

Perform the division. $2 x ^ { 2 } - 5 x + 5$ $Perform the division. 2 x ^ { 2 } - 5 x + 5$

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = 3 x ^ { 3 } + x + 3 ; k = 1$ $P ( 1 ) =$ __________

Solve: $\frac { 1 } { f } = \frac { 1 } { s _ { 1 } } + \frac { 1 } { s _ { 2 } }$ for $f$

Which of the following is a factor of $P ( x ) = 3 x ^ { 3 } + 8 x ^ { 2 } - 9 x - 18$ ?

Use synthetic division to perform the division. $\left( x ^ { 2 } - 3 x + 28 \right) \div ( x + 4 )$

Perform the indicated operation. Simplify, if possible. $\frac { 8 x ^ { 2 } + 2 x - 3 } { 8 x ^ { 2 } - 2 } \div \frac { 12 x + 9 } { 16 x ^ { 2 } + 12 x + 2 }$

Perform the operations and simplify the result when possible. $\frac { 8 x } { x + 1 } + \frac { 5 } { x + 1 } - \frac { 3 x } { x + 1 }$

Perform the indicated operation. Simplify, if possible. $\frac { 5 x + 1 } { x ^ { 2 } - 5 x - 14 } - \frac { x - 7 } { x ^ { 2 } - 5 x - 14 }$

Perform the operations and simplify the result when possible. $\frac { 2 } { a b ^ { 2 } } - \frac { 3 } { a ^ { 2 } b }$

Solve the formula for the indicated variable. $\frac { 1 } { q } + \frac { 1 } { p } = 1$ for q

Fill in the blank with the appropriate phrase. The least __________ of $\frac { x - 8 } { x + 4 }$ and $\frac { 4 - 5 x } { x }$ is $x ( x + 4 )$ .

Solve: $A = \frac { D } { B + C }$ for D .

Solve the equation and check the result. If the equation has no solution, answer none . $\frac { 1 } { 18 } + \frac { 1 } { n } - \frac { 2 } { 27 } = 0$ n= Find the extraneous solution. $n \neq$