Question 1

Solve the formula for the indicated variable. $\frac { p c } { s } = \frac { k } { n } \text { for }$

Accepted Answer

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

Question 2

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x + 1 ; P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 4 x - 20$ ( Hint : Write x+1 as $x - ( - 1 )$ .)

Accepted Answer

A)  yes 
B)  no 
A)  yes 
B)  no

Question 3

Perform the indicated operation. Simplify, if possible. $\frac { 2 x } { x ^ { 2 } - 16 } - \frac { 3 } { x ^ { 2 } - 5 x + 4 } + \frac { x + 1 } { x ^ { 2 } + 3 x - 4 }$

Accepted Answer

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

Question 4

Perform the division. $\frac { 35 a ^ { 3 } - 67 a ^ { 2 } + 36 } { 5 a - 6 }$

Accepted Answer

The answer of Perform the division. \(\frac { 35 a...

Question 5

Perform the indicated operation. Simplify, if possible. $\frac { 2 x } { x ^ { 2 } - x - 6 } + \frac { x } { x ^ { 2 } + 8 x + 12 }$

Accepted Answer

A)  $\frac { 3 x ^ { 2 } + 9 x } { ( x + 2 ) ( x - 3 ) ( x + 6 ) }$ 
B)  $\frac { 3 x } { ( x + 2 ) ( x - 3 ) ( x + 6 ) }$ 
C)  $\frac { 3 x ^ { 2 } + 15 x } { ( x + 2 ) ( x - 3 ) ( x + 6 ) }$ 
D)  $\frac { 3 x ^ { 2 } + 15 } { ( x + 2 ) ( x - 3 ) ( x + 6 ) }$ 
A)  $\frac { 3 x ^ { 2 } + 9 x } { ( x + 2 ) ( x - 3 ) ( x + 6 ) }$ 
B)  $\frac { 3 x } { ( x + 2 ) ( x - 3 ) ( x + 6 ) }$ 
C)  $\frac { 3 x ^ { 2 } + 15 x } { ( x + 2 ) ( x - 3 ) ( x + 6 ) }$ 
D)  $\frac { 3 x ^ { 2 } + 15 } { ( x + 2 ) ( x - 3 ) ( x + 6 ) }$

Question 6

A __________ is the quotient of two numbers or two quantities with the same units.

Accepted Answer

A)  variation 
B)  fraction 
C)  factor 
D)  proportion 
E)  ratio 
A)  variation 
B)  fraction 
C)  factor 
D)  proportion 
E)  ratio

Question 7

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

Accepted Answer

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

Question 8

Perform the indicated operation. Simplify, if possible. $\left( 4 x ^ { 2 } - 25 \right) \div \frac { 2 x ^ { 2 } - 3 x - 5 } { x + 4 } \div ( 2 x + 5 )$

Accepted Answer

A)  $\frac { ( 2 x + 5 ) ^ { 2 } ( x + 4 ) } { x + 1 }$ 
B)  $\frac { x + 1 } { x + 4 }$ 
C)  $\frac { x + 4 } { x + 1 }$ 
D)  $\frac { ( x + 4 ) } { ( 2 x - 5 ) ( 2 x + 5 ) ( x - 5 ) }$ 
A)  $\frac { ( 2 x + 5 ) ^ { 2 } ( x + 4 ) } { x + 1 }$ 
B)  $\frac { x + 1 } { x + 4 }$ 
C)  $\frac { x + 4 } { x + 1 }$ 
D)  $\frac { ( x + 4 ) } { ( 2 x - 5 ) ( 2 x + 5 ) ( x - 5 ) }$

Question 9

Solve the problem by writing a variation model. An object in free fall travels a distance s that is directly proportional to the square of the time t . If an object falls 960 feet in 8 seconds, how far will it fall in 10 seconds?

Accepted Answer

A)  1,260 ft 
B)  1,320 ft 
C)  1,440 ft 
D)  1,380 ft 
E)  1,500 ft 
A)  1,260 ft 
B)  1,320 ft 
C)  1,440 ft 
D)  1,380 ft 
E)  1,500 ft

Question 10

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = 3 x ^ { 3 } - 6 x ^ { 2 } + x + 2 ; \quad k = 1$

Accepted Answer

A)  3 
B)  2 
C)  1 
D)  0 
E)  -1 
A)  3 
B)  2 
C)  1 
D)  0 
E)  -1

Question 11

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

Accepted Answer

A)  $x + 5$ 
B)  $x - 5$ 
C)  $x + 4$ 
D)  $x - 4$ 
E)  $4 - x$ 
A)  $x + 5$ 
B)  $x - 5$ 
C)  $x + 4$ 
D)  $x - 4$ 
E)  $4 - x$

Question 12

Let $P ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 4 x - 5$ . Evaluate $P ( - 2 )$ by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division.

Accepted Answer

A)  -45 
B)  -44 
C) 44 
D)  -46 
E)  47 
A)  -45 
B)  -44 
C) 44 
D)  -46 
E)  47

Question 13

Perform the division. $\frac { 3 x ^ { 3 } - 8 x ^ { 2 } + x - 19 } { x - 3 }$

Accepted Answer

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

Question 14

Solve the formula for the indicated variable. $k = \frac { 2 A } { b + d }$ for A

Accepted Answer

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

Question 15

Divide: $\frac { 3 c ^ { 2 } - \frac { 1 } { 2 } c - 10 } { 2 c - 3 }$

Accepted Answer

The answer of Divide: \(\frac { 3 c ^ {...

Question 16

One crew can drywall a house in 7 days and another crew can drywall the same house in 9 days. If both crews work together, how long will it take to dry wall the house?

Accepted Answer

A)  8 days 
B)  6 days 
C)  $\frac { 63 } { 16 }$ days 
D)  $\frac { 7 } { 2 }$ days 
A)  8 days 
B)  6 days 
C)  $\frac { 63 } { 16 }$ days 
D)  $\frac { 7 } { 2 }$ days

Question 17

Solve: $\frac { 7 } { 2 x - 4 } + \frac { 1 } { 2 - x } = \frac { 5 } { 4 }$

Accepted Answer

The answer of Solve: \(\frac { 7 } { 2...

Question 18

Perform the division. $\frac { 10 x ^ { 3 } - 7 x ^ { 2 } - 10 x - 3 } { 2 x - 3 }$

Accepted Answer

The answer of Perform the division. \(\frac { 10 x...

Question 19

Divide using synthetic division: $\frac { 9 x ^ { 3 } - 4 x ^ { 2 } - 6 x + 5 } { x - 2 }$

Accepted Answer

A)  $9 x ^ { 2 } - 22 x + 38 - \frac { 81 } { x - 2 }$ 
B)  $9 x ^ { 2 } + 14 x + 22 + \frac { 49 } { x - 2 }$ 
C)  $9 x ^ { 2 } + 22 x + 38 + \frac { 81 } { x - 2 }$ 
D)  $9 x ^ { 2 } + 14 x + 22 + \frac { 39 } { x - 2 }$ 
A)  $9 x ^ { 2 } - 22 x + 38 - \frac { 81 } { x - 2 }$ 
B)  $9 x ^ { 2 } + 14 x + 22 + \frac { 49 } { x - 2 }$ 
C)  $9 x ^ { 2 } + 22 x + 38 + \frac { 81 } { x - 2 }$ 
D)  $9 x ^ { 2 } + 14 x + 22 + \frac { 39 } { x - 2 }$

Question 20

Solve the equation and check the result. If the equation has no solution, answer none . $\frac { 13 } { x - 5 } = \frac { 41 } { x ^ { 2 } - 25 } + \frac { 9 } { x + 5 }$

Accepted Answer

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

Solve the formula for the indicated variable. $\frac { p c } { s } = \frac { k } { n } \text { for }$

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x + 1 ; P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 4 x - 20$ ( Hint : Write x+1 as $x - ( - 1 )$ .)

Perform the indicated operation. Simplify, if possible. $\frac { 2 x } { x ^ { 2 } - 16 } - \frac { 3 } { x ^ { 2 } - 5 x + 4 } + \frac { x + 1 } { x ^ { 2 } + 3 x - 4 }$

Perform the division. $\frac { 35 a ^ { 3 } - 67 a ^ { 2 } + 36 } { 5 a - 6 }$

Perform the indicated operation. Simplify, if possible. $\frac { 2 x } { x ^ { 2 } - x - 6 } + \frac { x } { x ^ { 2 } + 8 x + 12 }$

A __________ is the quotient of two numbers or two quantities with the same units.

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

Perform the indicated operation. Simplify, if possible. $\left( 4 x ^ { 2 } - 25 \right) \div \frac { 2 x ^ { 2 } - 3 x - 5 } { x + 4 } \div ( 2 x + 5 )$

Solve the problem by writing a variation model. An object in free fall travels a distance s that is directly proportional to the square of the time t . If an object falls 960 feet in 8 seconds, how far will it fall in 10 seconds?

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = 3 x ^ { 3 } - 6 x ^ { 2 } + x + 2 ; \quad k = 1$

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

Let $P ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 4 x - 5$ . Evaluate $P ( - 2 )$ by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division.

Perform the division. $\frac { 3 x ^ { 3 } - 8 x ^ { 2 } + x - 19 } { x - 3 }$

Solve the formula for the indicated variable. $k = \frac { 2 A } { b + d }$ for A

Divide: $\frac { 3 c ^ { 2 } - \frac { 1 } { 2 } c - 10 } { 2 c - 3 }$

One crew can drywall a house in 7 days and another crew can drywall the same house in 9 days. If both crews work together, how long will it take to dry wall the house?

Solve: $\frac { 7 } { 2 x - 4 } + \frac { 1 } { 2 - x } = \frac { 5 } { 4 }$

Perform the division. $\frac { 10 x ^ { 3 } - 7 x ^ { 2 } - 10 x - 3 } { 2 x - 3 }$

Divide using synthetic division: $\frac { 9 x ^ { 3 } - 4 x ^ { 2 } - 6 x + 5 } { x - 2 }$

Solve the equation and check the result. If the equation has no solution, answer none . $\frac { 13 } { x - 5 } = \frac { 41 } { x ^ { 2 } - 25 } + \frac { 9 } { x + 5 }$

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

Solve the formula for the indicated variable. pcs=kn for \frac { p c } { s } = \frac { k } { n } \text { for }spc​=nk​ for

Use the factor theorem and determine whether the first expression is a factor of P ( x ). x+1;P(x)=x3+2x2−4x−20x + 1 ; P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 4 x - 20x+1;P(x)=x3+2x2−4x−20 ( Hint : Write x+1 as x−(−1)x - ( - 1 )x−(−1) .)

Perform the indicated operation. Simplify, if possible. 2xx2−16−3x2−5x+4+x+1x2+3x−4\frac { 2 x } { x ^ { 2 } - 16 } - \frac { 3 } { x ^ { 2 } - 5 x + 4 } + \frac { x + 1 } { x ^ { 2 } + 3 x - 4 }x2−162x​−x2−5x+43​+x2+3x−4x+1​

Perform the division. 35a3−67a2+365a−6\frac { 35 a ^ { 3 } - 67 a ^ { 2 } + 36 } { 5 a - 6 }5a−635a3−67a2+36​

Perform the indicated operation. Simplify, if possible. 2xx2−x−6+xx2+8x+12\frac { 2 x } { x ^ { 2 } - x - 6 } + \frac { x } { x ^ { 2 } + 8 x + 12 }x2−x−62x​+x2+8x+12x​

A __________ is the quotient of two numbers or two quantities with the same units.

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

Perform the indicated operation. Simplify, if possible. (4x2−25)÷2x2−3x−5x+4÷(2x+5)\left( 4 x ^ { 2 } - 25 \right) \div \frac { 2 x ^ { 2 } - 3 x - 5 } { x + 4 } \div ( 2 x + 5 )(4x2−25)÷x+42x2−3x−5​÷(2x+5)

Solve the problem by writing a variation model. An object in free fall travels a distance s that is directly proportional to the square of the time t . If an object falls 960 feet in 8 seconds, how far will it fall in 10 seconds?

Use the remainder theorem and synthetic division to find P ( k ). P(x)=3x3−6x2+x+2;k=1P ( x ) = 3 x ^ { 3 } - 6 x ^ { 2 } + x + 2 ; \quad k = 1P(x)=3x3−6x2+x+2;k=1

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

Let P(x)=3x3−2x2+4x−5P ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 4 x - 5P(x)=3x3−2x2+4x−5 . Evaluate P(−2)P ( - 2 )P(−2) by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division.

Perform the division. 3x3−8x2+x−19x−3\frac { 3 x ^ { 3 } - 8 x ^ { 2 } + x - 19 } { x - 3 }x−33x3−8x2+x−19​

Solve the formula for the indicated variable. k=2Ab+dk = \frac { 2 A } { b + d }k=b+d2A​ for A

Divide: 3c2−12c−102c−3\frac { 3 c ^ { 2 } - \frac { 1 } { 2 } c - 10 } { 2 c - 3 }2c−33c2−21​c−10​

One crew can drywall a house in 7 days and another crew can drywall the same house in 9 days. If both crews work together, how long will it take to dry wall the house?

Solve: 72x−4+12−x=54\frac { 7 } { 2 x - 4 } + \frac { 1 } { 2 - x } = \frac { 5 } { 4 }2x−47​+2−x1​=45​

Perform the division. 10x3−7x2−10x−32x−3\frac { 10 x ^ { 3 } - 7 x ^ { 2 } - 10 x - 3 } { 2 x - 3 }2x−310x3−7x2−10x−3​

Divide using synthetic division: 9x3−4x2−6x+5x−2\frac { 9 x ^ { 3 } - 4 x ^ { 2 } - 6 x + 5 } { x - 2 }x−29x3−4x2−6x+5​

Solve the equation and check the result. If the equation has no solution, answer none . 13x−5=41x2−25+9x+5\frac { 13 } { x - 5 } = \frac { 41 } { x ^ { 2 } - 25 } + \frac { 9 } { x + 5 }x−513​=x2−2541​+x+59​

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

Solve the formula for the indicated variable. $\frac { p c } { s } = \frac { k } { n } \text { for }$

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x + 1 ; P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 4 x - 20$ ( Hint : Write x+1 as $x - ( - 1 )$ .)

Perform the indicated operation. Simplify, if possible. $\frac { 2 x } { x ^ { 2 } - 16 } - \frac { 3 } { x ^ { 2 } - 5 x + 4 } + \frac { x + 1 } { x ^ { 2 } + 3 x - 4 }$

Perform the division. $\frac { 35 a ^ { 3 } - 67 a ^ { 2 } + 36 } { 5 a - 6 }$

Perform the indicated operation. Simplify, if possible. $\frac { 2 x } { x ^ { 2 } - x - 6 } + \frac { x } { x ^ { 2 } + 8 x + 12 }$

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

Perform the indicated operation. Simplify, if possible. $\left( 4 x ^ { 2 } - 25 \right) \div \frac { 2 x ^ { 2 } - 3 x - 5 } { x + 4 } \div ( 2 x + 5 )$

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = 3 x ^ { 3 } - 6 x ^ { 2 } + x + 2 ; \quad k = 1$

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

Let $P ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 4 x - 5$ . Evaluate $P ( - 2 )$ by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division.

Perform the division. $\frac { 3 x ^ { 3 } - 8 x ^ { 2 } + x - 19 } { x - 3 }$

Solve the formula for the indicated variable. $k = \frac { 2 A } { b + d }$ for A

Divide: $\frac { 3 c ^ { 2 } - \frac { 1 } { 2 } c - 10 } { 2 c - 3 }$

Solve: $\frac { 7 } { 2 x - 4 } + \frac { 1 } { 2 - x } = \frac { 5 } { 4 }$

Perform the division. $\frac { 10 x ^ { 3 } - 7 x ^ { 2 } - 10 x - 3 } { 2 x - 3 }$

Divide using synthetic division: $\frac { 9 x ^ { 3 } - 4 x ^ { 2 } - 6 x + 5 } { x - 2 }$

Solve the equation and check the result. If the equation has no solution, answer none . $\frac { 13 } { x - 5 } = \frac { 41 } { x ^ { 2 } - 25 } + \frac { 9 } { x + 5 }$