Question 1

A room should have at least 108 square feet of windows for natural light. Convert this to square yards. __________ $\mathrm { yd } ^ { 2 }$

Accepted Answer

The answer of A room should have at least 108...

Question 2

Perform the operations and simplify the result when possible. $\frac { 4 } { a b ^ { 2 } } - \frac { 7 } { a ^ { 2 } b }$

Accepted Answer

A)  $- \frac { 3 ( a - b ) } { a ^ { 2 } b ^ { 2 } }$ 
B)  $\frac { 4 a - 7 b } { a b ^ { 2 } }$ 
C)  $- \frac { 3 a b } { a ^ { 2 } b ^ { 2 } }$ 
D)  $\frac { 4 a - 7 b } { a ^ { 2 } b ^ { 2 } }$ 
E)  $\frac { 4 a - 7 b } { a b }$ 
A)  $- \frac { 3 ( a - b ) } { a ^ { 2 } b ^ { 2 } }$ 
B)  $\frac { 4 a - 7 b } { a b ^ { 2 } }$ 
C)  $- \frac { 3 a b } { a ^ { 2 } b ^ { 2 } }$ 
D)  $\frac { 4 a - 7 b } { a ^ { 2 } b ^ { 2 } }$ 
E)  $\frac { 4 a - 7 b } { a b }$

Question 3

Perform the division. $\frac { x ^ { 2 } + 9 x + 20 } { x + 5 }$

Accepted Answer

The answer of Perform the division. \(\frac { x ^...

Question 4

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

Accepted Answer

A)  $\frac { x - 3 } { ( x - 7 ) ( 7 x - 1 ) }$ 
B)  $\frac { x + 7 x - 15 } { ( x - 7 ) ( 7 x - 1 ) }$ 
C)  $\frac { ( x - 3 ) ( x + 5 ) } { ( x - 7 ) ( 7 x - 1 ) }$ 
D)  $\frac { x + 3 } { 8 x - 8 }$ 
A)  $\frac { x - 3 } { ( x - 7 ) ( 7 x - 1 ) }$ 
B)  $\frac { x + 7 x - 15 } { ( x - 7 ) ( 7 x - 1 ) }$ 
C)  $\frac { ( x - 3 ) ( x + 5 ) } { ( x - 7 ) ( 7 x - 1 ) }$ 
D)  $\frac { x + 3 } { 8 x - 8 }$

Question 5

Express the verbal model " M varies inversely with the cube of n and directly with the square of x " into symbols.

Accepted Answer

A)  M = $\frac { K x ^ { 2 } } { n ^ { 3 } }$ 
B)  M = $\frac { K n ^ { 3 } } { x ^ { 2 } }$ 
C)  $M = k x ^ { 2 } n ^ { 3 }$ 
D)  M = $\frac { K \sqrt { x } } { \sqrt [ 3 ] { n } }$ 
A)  M = $\frac { K x ^ { 2 } } { n ^ { 3 } }$ 
B)  M = $\frac { K n ^ { 3 } } { x ^ { 2 } }$ 
C)  $M = k x ^ { 2 } n ^ { 3 }$ 
D)  M = $\frac { K \sqrt { x } } { \sqrt [ 3 ] { n } }$

Question 6

Find the power: $\left( \frac { 4 x + 5 } { x ^ { 2 } - 4 } \right) ^ { 2 }$

Accepted Answer

The answer of Find the power: \(\left( \frac { 4...

Question 7

By the __________ theorem, if a polynomial P ( x ) is divided by $x - k$ , the remainder is P ( k ).

Accepted Answer

By the **Remainder**

Question 8

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

Accepted Answer

A)  $\frac { 2 d } { c ^ { 2 } + d ^ { 2 } }$ 
B)  $\frac { 2 c } { c + d }$ 
C)  $\frac { 2 d } { c + d }$ 
D)  $\frac { 2 c } { c ^ { 2 } + d ^ { 2 } }$ 
E)  $\frac { 2 d } { c ^ { 2 } - d ^ { 2 } }$ 
A)  $\frac { 2 d } { c ^ { 2 } + d ^ { 2 } }$ 
B)  $\frac { 2 c } { c + d }$ 
C)  $\frac { 2 d } { c + d }$ 
D)  $\frac { 2 c } { c ^ { 2 } + d ^ { 2 } }$ 
E)  $\frac { 2 d } { c ^ { 2 } - d ^ { 2 } }$

Question 9

Solve: $\frac { x } { x + 8 } - \frac { 2 } { x - 2 } = \frac { 16 } { x ^ { 2 } + 6 x - 16 }$

Accepted Answer

A)  $\{ - 4,8 \}$ 
B)  {18} 
C)  {6} 
D)  no solution 
A)  $\{ - 4,8 \}$ 
B)  {18} 
C)  {6} 
D)  no solution

Question 10

Perform the operations and simplify the result when possible. $\frac { x + 9 } { x + 5 } - \frac { x - 10 } { x + 7 }$

Accepted Answer

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

Question 11

Insert either a multiplication symbol . or a division symbol ÷ in each blank to make a true statement. $\frac { y ^ { 2 } } { x ^ { 2 } } $⎯⎯⎯⎯$ \frac { x ^ { 2 } } { y } $⎯⎯⎯⎯⎯ $\frac { x } { y ^ { 2 } } = \frac { y } { x ^ { 3 } }$

Accepted Answer

The answer of Insert either a multiplication symbol . or...

Question 12

Solve the formula for the indicated variable. $T = \frac { 3 Q } { W - n }$ for $Q$

Accepted Answer

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

Question 13

Determine if x-1 is a factor of $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - x + 5$

Accepted Answer

A)  factor 
B)  not a factor 
A)  factor 
B)  not a factor

Question 14

A father can paint a bedroom in 3 hours. His son can paint the bedroom in 4 hours. If they work together, how long will it take them to paint the bedroom?

Accepted Answer

The answer of A father can paint a bedroom in...

Question 15

Perform the indicated operation. Simplify, if possible. $\frac { 2 y ^ { 2 } - 18 } { 6 y - 12 } \cdot \frac { y ^ { 2 } - 5 y + 6 } { y ^ { 2 } - 6 y + 9 }$

Accepted Answer

A)  $\frac { y + 3 } { 3 }$ 
B)  $9 y - 1$ 
C)  $\frac { y - 9 } { y - 3 }$ 
D)  $y + 3$ 
A)  $\frac { y + 3 } { 3 }$ 
B)  $9 y - 1$ 
C)  $\frac { y - 9 } { y - 3 }$ 
D)  $y + 3$

Question 16

Perform the operations and simplify the result when possible. $\frac { 2 x } { x ^ { 2 } + 13 x + 22 } + \frac { 2 x } { x ^ { 2 } - 4 }$

Accepted Answer

A)  $\begin{array} { r } 
2 x - 9 \
\hline ( x + 11 ) ( x - 2 ) ( x + 2 )
\end{array}$ 
B)  $\frac { 2 x ( 2 x + 9 ) } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$ 
C)  $\frac { 2 x ( 2 x + 11 ) } { ( x + 9 ) ( x - 2 ) ( x + 2 ) }$ 
D)  $\frac { 2 x + 9 } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$ 
E)  $\frac { 2 x ( 2 x - 9 ) } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$ 
A)  $\begin{array} { r } 
2 x - 9 \
\hline ( x + 11 ) ( x - 2 ) ( x + 2 )
\end{array}$ 
B)  $\frac { 2 x ( 2 x + 9 ) } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$ 
C)  $\frac { 2 x ( 2 x + 11 ) } { ( x + 9 ) ( x - 2 ) ( x + 2 ) }$ 
D)  $\frac { 2 x + 9 } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$ 
E)  $\frac { 2 x ( 2 x - 9 ) } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$

Question 17

Perform the division. $3 x ^ { 2 } - 7 x + 6 $

Accepted Answer

The answer of Perform the division. \(3 x ^ {...

Question 18

The __________ of $\frac { a + 2 } { a + 4 } \text { is } \frac { a + 4 } { a + 2 }$ .

Accepted Answer

The answer of The __________ of \(\frac { a +...

Question 19

Use synthetic division to perform the division. $\left( 3 x ^ { 2 } - 14 x + 15 \right) \div ( x - 3 )$

Accepted Answer

The answer of Use synthetic division to perform the division....

Question 20

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = x ^ { 3 } + x ^ { 2 } + 14 ; k = - 3$ $P ( - 3 ) =$ __________

Accepted Answer

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

A room should have at least 108 square feet of windows for natural light. Convert this to square yards. __________ $\mathrm { yd } ^ { 2 }$

Perform the operations and simplify the result when possible. $\frac { 4 } { a b ^ { 2 } } - \frac { 7 } { a ^ { 2 } b }$

Perform the division. $\frac { x ^ { 2 } + 9 x + 20 } { x + 5 }$

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

Express the verbal model " M varies inversely with the cube of n and directly with the square of x " into symbols.

Find the power: $\left( \frac { 4 x + 5 } { x ^ { 2 } - 4 } \right) ^ { 2 }$

By the __________ theorem, if a polynomial P ( x ) is divided by $x - k$ , the remainder is P ( k ).

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

Solve: $\frac { x } { x + 8 } - \frac { 2 } { x - 2 } = \frac { 16 } { x ^ { 2 } + 6 x - 16 }$

Perform the operations and simplify the result when possible. $\frac { x + 9 } { x + 5 } - \frac { x - 10 } { x + 7 }$

Insert either a multiplication symbol . or a division symbol ÷ in each blank to make a true statement. $\frac { y ^ { 2 } } { x ^ { 2 } }$ ⎯⎯⎯⎯ $\frac { x ^ { 2 } } { y }$ ⎯⎯⎯⎯⎯ $\frac { x } { y ^ { 2 } } = \frac { y } { x ^ { 3 } }$

Solve the formula for the indicated variable. $T = \frac { 3 Q } { W - n }$ for $Q$

Determine if x-1 is a factor of $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - x + 5$

A father can paint a bedroom in 3 hours. His son can paint the bedroom in 4 hours. If they work together, how long will it take them to paint the bedroom?

Perform the indicated operation. Simplify, if possible. $\frac { 2 y ^ { 2 } - 18 } { 6 y - 12 } \cdot \frac { y ^ { 2 } - 5 y + 6 } { y ^ { 2 } - 6 y + 9 }$

Perform the operations and simplify the result when possible. $\frac { 2 x } { x ^ { 2 } + 13 x + 22 } + \frac { 2 x } { x ^ { 2 } - 4 }$

Perform the division. $3 x ^ { 2 } - 7 x + 6$ $Perform the division. 3 x ^ { 2 } - 7 x + 6$

The __________ of $\frac { a + 2 } { a + 4 } \text { is } \frac { a + 4 } { a + 2 }$ .

Use synthetic division to perform the division. $\left( 3 x ^ { 2 } - 14 x + 15 \right) \div ( x - 3 )$

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = x ^ { 3 } + x ^ { 2 } + 14 ; k = - 3$ $P ( - 3 ) =$ __________

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

A room should have at least 108 square feet of windows for natural light. Convert this to square yards. __________ yd2\mathrm { yd } ^ { 2 }yd2

Perform the operations and simplify the result when possible. 4ab2−7a2b\frac { 4 } { a b ^ { 2 } } - \frac { 7 } { a ^ { 2 } b }ab24​−a2b7​

Perform the division. x2+9x+20x+5\frac { x ^ { 2 } + 9 x + 20 } { x + 5 }x+5x2+9x+20​

Perform the indicated operation. Simplify, if possible. 1x−7+x+27x−1\frac { 1 } { x - 7 } + \frac { x + 2 } { 7 x - 1 }x−71​+7x−1x+2​

Express the verbal model " M varies inversely with the cube of n and directly with the square of x " into symbols.

Find the power: (4x+5x2−4)2\left( \frac { 4 x + 5 } { x ^ { 2 } - 4 } \right) ^ { 2 }(x2−44x+5​)2

By the __________ theorem, if a polynomial P ( x ) is divided by x−kx - kx−k , the remainder is P ( k ).

Perform the operations and simplify the result when possible. cc−d+dc+d−c2+d2a2−b2\frac { c } { c - d } + \frac { d } { c + d } - \frac { c ^ { 2 } + d ^ { 2 } } { a ^ { 2 } - b ^ { 2 } }c−dc​+c+dd​−a2−b2c2+d2​

Solve: xx+8−2x−2=16x2+6x−16\frac { x } { x + 8 } - \frac { 2 } { x - 2 } = \frac { 16 } { x ^ { 2 } + 6 x - 16 }x+8x​−x−22​=x2+6x−1616​

Perform the operations and simplify the result when possible. x+9x+5−x−10x+7\frac { x + 9 } { x + 5 } - \frac { x - 10 } { x + 7 }x+5x+9​−x+7x−10​

Insert either a multiplication symbol . or a division symbol ÷ in each blank to make a true statement. y2x2\frac { y ^ { 2 } } { x ^ { 2 } } x2y2​ ⎯⎯⎯⎯ x2y \frac { x ^ { 2 } } { y } yx2​ ⎯⎯⎯⎯⎯ xy2=yx3\frac { x } { y ^ { 2 } } = \frac { y } { x ^ { 3 } }y2x​=x3y​

Solve the formula for the indicated variable. T=3QW−nT = \frac { 3 Q } { W - n }T=W−n3Q​ for QQQ

Determine if x-1 is a factor of P(x)=x3−5x2−x+5P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - x + 5P(x)=x3−5x2−x+5

A father can paint a bedroom in 3 hours. His son can paint the bedroom in 4 hours. If they work together, how long will it take them to paint the bedroom?

Perform the indicated operation. Simplify, if possible. 2y2−186y−12⋅y2−5y+6y2−6y+9\frac { 2 y ^ { 2 } - 18 } { 6 y - 12 } \cdot \frac { y ^ { 2 } - 5 y + 6 } { y ^ { 2 } - 6 y + 9 }6y−122y2−18​⋅y2−6y+9y2−5y+6​

Perform the operations and simplify the result when possible. 2xx2+13x+22+2xx2−4\frac { 2 x } { x ^ { 2 } + 13 x + 22 } + \frac { 2 x } { x ^ { 2 } - 4 }x2+13x+222x​+x2−42x​

Perform the division. 3x2−7x+63 x ^ { 2 } - 7 x + 6 3x2−7x+6

The __________ of a+2a+4 is a+4a+2\frac { a + 2 } { a + 4 } \text { is } \frac { a + 4 } { a + 2 }a+4a+2​ is a+2a+4​ .

Use synthetic division to perform the division. (3x2−14x+15)÷(x−3)\left( 3 x ^ { 2 } - 14 x + 15 \right) \div ( x - 3 )(3x2−14x+15)÷(x−3)

Use the remainder theorem and synthetic division to find P ( k ). P(x)=x3+x2+14;k=−3P ( x ) = x ^ { 3 } + x ^ { 2 } + 14 ; k = - 3P(x)=x3+x2+14;k=−3 P(−3)=P ( - 3 ) =P(−3)= __________

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

A room should have at least 108 square feet of windows for natural light. Convert this to square yards. __________ $\mathrm { yd } ^ { 2 }$

Perform the operations and simplify the result when possible. $\frac { 4 } { a b ^ { 2 } } - \frac { 7 } { a ^ { 2 } b }$

Perform the division. $\frac { x ^ { 2 } + 9 x + 20 } { x + 5 }$

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

Find the power: $\left( \frac { 4 x + 5 } { x ^ { 2 } - 4 } \right) ^ { 2 }$

By the __________ theorem, if a polynomial P ( x ) is divided by $x - k$ , the remainder is P ( k ).

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

Solve: $\frac { x } { x + 8 } - \frac { 2 } { x - 2 } = \frac { 16 } { x ^ { 2 } + 6 x - 16 }$

Perform the operations and simplify the result when possible. $\frac { x + 9 } { x + 5 } - \frac { x - 10 } { x + 7 }$

Insert either a multiplication symbol . or a division symbol ÷ in each blank to make a true statement. $\frac { y ^ { 2 } } { x ^ { 2 } }$ ⎯⎯⎯⎯ $\frac { x ^ { 2 } } { y }$ ⎯⎯⎯⎯⎯ $\frac { x } { y ^ { 2 } } = \frac { y } { x ^ { 3 } }$

Solve the formula for the indicated variable. $T = \frac { 3 Q } { W - n }$ for $Q$

Determine if x-1 is a factor of $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - x + 5$

Perform the indicated operation. Simplify, if possible. $\frac { 2 y ^ { 2 } - 18 } { 6 y - 12 } \cdot \frac { y ^ { 2 } - 5 y + 6 } { y ^ { 2 } - 6 y + 9 }$

Perform the operations and simplify the result when possible. $\frac { 2 x } { x ^ { 2 } + 13 x + 22 } + \frac { 2 x } { x ^ { 2 } - 4 }$

Perform the division. $3 x ^ { 2 } - 7 x + 6$ $Perform the division. 3 x ^ { 2 } - 7 x + 6$

The __________ of $\frac { a + 2 } { a + 4 } \text { is } \frac { a + 4 } { a + 2 }$ .

Use synthetic division to perform the division. $\left( 3 x ^ { 2 } - 14 x + 15 \right) \div ( x - 3 )$

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = x ^ { 3 } + x ^ { 2 } + 14 ; k = - 3$ $P ( - 3 ) =$ __________