Question 1

Perform the division. $\frac { 38 x ^ { 5 } y ^ { 6 } - 19 x ^ { 4 } y ^ { 11 } + 57 x y } { 76 x ^ { 2 } y ^ { 4 } }$

Accepted Answer

A)  $\frac { x ^ { 4 } y ^ { 2 } } { 2 } - \frac { x ^ { 2 } y ^ { 7 } } { 4 } + \frac { 3 } { 4 x y ^ { 3 } }$ 
B)  $\frac { x ^ { 3 } y ^ { 2 } } { 2 } - \frac { x ^ { 2 } y ^ { 6 } } { 4 } + \frac { 3 } { 4 x y ^ { 3 } }$ 
C)  $\frac { x ^ { 3 } y ^ { 2 } } { 2 } - \frac { x ^ { 2 } y ^ { 5 } } { 4 } + \frac { 3 } { 4 x y ^ { 3 } }$ 
D)  $\frac { x ^ { 3 } y ^ { 2 } } { 2 } - \frac { x ^ { 2 } y ^ { 7 } } { 4 } + \frac { 3 } { 4 x y ^ { 3 } }$ 
E)  $\frac { x ^ { 3 } y ^ { 3 } } { 2 } - \frac { x ^ { 2 } y ^ { 7 } } { 4 } + \frac { 3 } { 4 x y ^ { 3 } }$ 
A)  $\frac { x ^ { 4 } y ^ { 2 } } { 2 } - \frac { x ^ { 2 } y ^ { 7 } } { 4 } + \frac { 3 } { 4 x y ^ { 3 } }$ 
B)  $\frac { x ^ { 3 } y ^ { 2 } } { 2 } - \frac { x ^ { 2 } y ^ { 6 } } { 4 } + \frac { 3 } { 4 x y ^ { 3 } }$ 
C)  $\frac { x ^ { 3 } y ^ { 2 } } { 2 } - \frac { x ^ { 2 } y ^ { 5 } } { 4 } + \frac { 3 } { 4 x y ^ { 3 } }$ 
D)  $\frac { x ^ { 3 } y ^ { 2 } } { 2 } - \frac { x ^ { 2 } y ^ { 7 } } { 4 } + \frac { 3 } { 4 x y ^ { 3 } }$ 
E)  $\frac { x ^ { 3 } y ^ { 3 } } { 2 } - \frac { x ^ { 2 } y ^ { 7 } } { 4 } + \frac { 3 } { 4 x y ^ { 3 } }$

Question 2

The first bird can fly about 15 mph faster than the second one. In the same time that the first bird travels 110 miles, the second bird travels 60 miles. Find their flying speeds.

Accepted Answer

The first

Question 3

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

Accepted Answer

The answer of Let \(P ( x ) = 2...

Question 4

Divide: $\frac { 1.2 x ^ { 3 } + 0.1 x ^ { 2 } + 0.2 x - 0.2 } { 0.4 x + 0.3 }$

Accepted Answer

The answer of Divide: \(\frac { 1.2 x ^ {...

Question 5

Perform the indicated operation. Simplify, if possible. $\frac { 2 x ^ { 2 } - 8 } { 10 x ^ { 2 } - 15 x - 10 } \div \frac { x ^ { 2 } + 4 x + 4 } { 4 x + 2 }$

Accepted Answer

A)  $\frac { ( x + 2 ) ^ { 3 } } { 5 ( 2 x + 1 ) ^ { 2 } }$ 
B)  $\frac { 2 ( 2 x - 4 ) ( 2 x + 1 ) } { ( 10 x + 5 ) ( x + 2 ) ^ { 2 } }$ 
C)  $\frac { 4 ( x - 2 ) ( 2 x + 1 ) } { 5 ( 2 x - 1 ) ( x + 2 ) ^ { 2 } }$ 
D)  $\frac { 4 } { 5 ( x + 2 ) }$ 
A)  $\frac { ( x + 2 ) ^ { 3 } } { 5 ( 2 x + 1 ) ^ { 2 } }$ 
B)  $\frac { 2 ( 2 x - 4 ) ( 2 x + 1 ) } { ( 10 x + 5 ) ( x + 2 ) ^ { 2 } }$ 
C)  $\frac { 4 ( x - 2 ) ( 2 x + 1 ) } { 5 ( 2 x - 1 ) ( x + 2 ) ^ { 2 } }$ 
D)  $\frac { 4 } { 5 ( x + 2 ) }$

Question 6

Use synthetic division to perform the division. $\left( m ^ { 3 } - m ^ { 2 } - m - 2 \right) \div ( m + 1 )$

Accepted Answer

A)  $m ^ { 2 } - 2 m + 1 + \frac { 3 } { m + 1 }$ 
B)  $m ^ { 2 } - 2 m + 1 - \frac { 3 } { m + 1 }$ 
C)  $m ^ { 2 } - 2 m + 1 - \frac { 3 } { m - 1 }$ 
D)  $m ^ { 2 } - 2 m + 2 - \frac { 3 } { m + 1 }$ 
E)  $m ^ { 2 } + 2 m + 1 - \frac { 3 } { m + 1 }$ 
A)  $m ^ { 2 } - 2 m + 1 + \frac { 3 } { m + 1 }$ 
B)  $m ^ { 2 } - 2 m + 1 - \frac { 3 } { m + 1 }$ 
C)  $m ^ { 2 } - 2 m + 1 - \frac { 3 } { m - 1 }$ 
D)  $m ^ { 2 } - 2 m + 2 - \frac { 3 } { m + 1 }$ 
E)  $m ^ { 2 } + 2 m + 1 - \frac { 3 } { m + 1 }$

Question 7

If P ( x ) is a polynomial and if $P ( k ) = 0$ , then k is called a __________ of the polynomial.

Accepted Answer

If P(x) is a polynom

Question 8

Solve the proportion. $\frac { 1 } { x + 2 } = \frac { - 2 x } { x + 3 }$

Accepted Answer

A)  x=1 
B)  $x = - \frac { 3 } { 2 } , x = - 1$ 
C)  $x = - \frac { 2 } { 5 } , x = - 6$ 
D)  $x = 6 , x = - 2$ 
E)  no solution 
A)  x=1 
B)  $x = - \frac { 3 } { 2 } , x = - 1$ 
C)  $x = - \frac { 2 } { 5 } , x = - 6$ 
D)  $x = 6 , x = - 2$ 
E)  no solution

Question 9

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

Accepted Answer

A)  divisor 
B)  factor 
C)  remainder 
D)  synthetic 
E)  binomial 
A)  divisor 
B)  factor 
C)  remainder 
D)  synthetic 
E)  binomial

Question 10

Divide: $\frac { 27 x y ^ { 2 } - 12 x ^ { 3 } y ^ { 5 } } { 9 x ^ { 3 } y ^ { 5 } }$

Accepted Answer

A)  $3 x ^ { 2 } y ^ { 3 } - \frac { 4 } { 3 }$ 
B)  $\frac { 1 } { 3 x ^ { 2 } y ^ { 3 } } - \frac { 4 } { 3 }$ 
C)  $\frac { 3 } { x ^ { 2 } y ^ { 3 } } - \frac { 4 } { 3 }$ 
D)  $\frac { 5 x y ^ { 2 } } { 3 }$ 
A)  $3 x ^ { 2 } y ^ { 3 } - \frac { 4 } { 3 }$ 
B)  $\frac { 1 } { 3 x ^ { 2 } y ^ { 3 } } - \frac { 4 } { 3 }$ 
C)  $\frac { 3 } { x ^ { 2 } y ^ { 3 } } - \frac { 4 } { 3 }$ 
D)  $\frac { 5 x y ^ { 2 } } { 3 }$

Question 11

One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 8 hours. How long will it take the pipe to fill the pool if the drain is left open?
 __________ hr

Accepted Answer

The answer of One inlet pipe can fill an empty...

Question 12

Perform the division. $\frac { 2 x ^ { 3 } - 3 x ^ { 2 } + x - 13 } { x - 2 }$

Accepted Answer

A)  $2 x ^ { 2 } + x + 4 - \frac { 10 } { x - 2 }$ 
B)  $2 x ^ { 2 } + x + 3 - \frac { 7 } { x - 2 }$ 
C)  $2 x ^ { 2 } + x + 3$ 
D)  $2 x ^ { 2 } + x + 3 - \frac { 9 } { x - 2 }$ 
E)  $2 x ^ { 2 } + x + 4 - \frac { 8 } { x - 2 }$ 
A)  $2 x ^ { 2 } + x + 4 - \frac { 10 } { x - 2 }$ 
B)  $2 x ^ { 2 } + x + 3 - \frac { 7 } { x - 2 }$ 
C)  $2 x ^ { 2 } + x + 3$ 
D)  $2 x ^ { 2 } + x + 3 - \frac { 9 } { x - 2 }$ 
E)  $2 x ^ { 2 } + x + 4 - \frac { 8 } { x - 2 }$

Question 13

Solve: $\frac { 1 } { 3 } - \frac { 3 } { 2 x } = \frac { 3 } { x ^ { 2 } }$

Accepted Answer

A)  $\left\{ - 6 , \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ \frac { 9 } { 2 } , 18 \right\}$ 
C)  $\left\{ - \frac { 9 } { 2 } , - 18 \right\}$ 
D)  $\left\{ 6 , - \frac { 3 } { 2 } \right\}$ 
A)  $\left\{ - 6 , \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ \frac { 9 } { 2 } , 18 \right\}$ 
C)  $\left\{ - \frac { 9 } { 2 } , - 18 \right\}$ 
D)  $\left\{ 6 , - \frac { 3 } { 2 } \right\}$

Question 14

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

Accepted Answer

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

Question 15

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x + 2 ; P ( x ) = 4 x ^ { 2 } + 8 x + 3$ ( Hint : Write x+2 as $x - ( - 2 )$ .)

Accepted Answer

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

Question 16

Solve the problem by writing a variation model. The distance that a car can go varies directly with the number of gallons of gasoline it consumes. If a car can go 312 miles on 13 gallons of gasoline, how far can it go on a full tank of 18 gallons?
 __________ mi

Accepted Answer

The answer of Solve the problem by writing a variation...

Question 17

Perform the operations and simplify the result when possible. $\frac { 5 } { x + 1 } - \frac { 4 } { x - 1 } + \frac { x + 7 } { x ^ { 2 } - 1 }$

Accepted Answer

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

Perform the division. $\frac { 38 x ^ { 5 } y ^ { 6 } - 19 x ^ { 4 } y ^ { 11 } + 57 x y } { 76 x ^ { 2 } y ^ { 4 } }$

The first bird can fly about 15 mph faster than the second one. In the same time that the first bird travels 110 miles, the second bird travels 60 miles. Find their flying speeds.

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

Divide: $\frac { 1.2 x ^ { 3 } + 0.1 x ^ { 2 } + 0.2 x - 0.2 } { 0.4 x + 0.3 }$

Perform the indicated operation. Simplify, if possible. $\frac { 2 x ^ { 2 } - 8 } { 10 x ^ { 2 } - 15 x - 10 } \div \frac { x ^ { 2 } + 4 x + 4 } { 4 x + 2 }$

Use synthetic division to perform the division. $\left( m ^ { 3 } - m ^ { 2 } - m - 2 \right) \div ( m + 1 )$

If P ( x ) is a polynomial and if $P ( k ) = 0$ , then k is called a __________ of the polynomial.

Solve the proportion. $\frac { 1 } { x + 2 } = \frac { - 2 x } { x + 3 }$

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

Divide: $\frac { 27 x y ^ { 2 } - 12 x ^ { 3 } y ^ { 5 } } { 9 x ^ { 3 } y ^ { 5 } }$

One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 8 hours. How long will it take the pipe to fill the pool if the drain is left open? __________ hr

Perform the division. $\frac { 2 x ^ { 3 } - 3 x ^ { 2 } + x - 13 } { x - 2 }$

Solve: $\frac { 1 } { 3 } - \frac { 3 } { 2 x } = \frac { 3 } { x ^ { 2 } }$

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

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x + 2 ; P ( x ) = 4 x ^ { 2 } + 8 x + 3$ ( Hint : Write x+2 as $x - ( - 2 )$ .)

Solve the problem by writing a variation model. The distance that a car can go varies directly with the number of gallons of gasoline it consumes. If a car can go 312 miles on 13 gallons of gasoline, how far can it go on a full tank of 18 gallons? __________ mi

Perform the operations and simplify the result when possible. $\frac { 5 } { x + 1 } - \frac { 4 } { x - 1 } + \frac { x + 7 } { x ^ { 2 } - 1 }$

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

Perform the division. 38x5y6−19x4y11+57xy76x2y4\frac { 38 x ^ { 5 } y ^ { 6 } - 19 x ^ { 4 } y ^ { 11 } + 57 x y } { 76 x ^ { 2 } y ^ { 4 } }76x2y438x5y6−19x4y11+57xy​

The first bird can fly about 15 mph faster than the second one. In the same time that the first bird travels 110 miles, the second bird travels 60 miles. Find their flying speeds.

Divide: 1.2x3+0.1x2+0.2x−0.20.4x+0.3\frac { 1.2 x ^ { 3 } + 0.1 x ^ { 2 } + 0.2 x - 0.2 } { 0.4 x + 0.3 }0.4x+0.31.2x3+0.1x2+0.2x−0.2​

Perform the indicated operation. Simplify, if possible. 2x2−810x2−15x−10÷x2+4x+44x+2\frac { 2 x ^ { 2 } - 8 } { 10 x ^ { 2 } - 15 x - 10 } \div \frac { x ^ { 2 } + 4 x + 4 } { 4 x + 2 }10x2−15x−102x2−8​÷4x+2x2+4x+4​

Use synthetic division to perform the division. (m3−m2−m−2)÷(m+1)\left( m ^ { 3 } - m ^ { 2 } - m - 2 \right) \div ( m + 1 )(m3−m2−m−2)÷(m+1)

If P ( x ) is a polynomial and if P(k)=0P ( k ) = 0P(k)=0 , then k is called a __________ of the polynomial.

Solve the proportion. 1x+2=−2xx+3\frac { 1 } { x + 2 } = \frac { - 2 x } { x + 3 }x+21​=x+3−2x​

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

Divide: 27xy2−12x3y59x3y5\frac { 27 x y ^ { 2 } - 12 x ^ { 3 } y ^ { 5 } } { 9 x ^ { 3 } y ^ { 5 } }9x3y527xy2−12x3y5​

One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 8 hours. How long will it take the pipe to fill the pool if the drain is left open? __________ hr

Perform the division. 2x3−3x2+x−13x−2\frac { 2 x ^ { 3 } - 3 x ^ { 2 } + x - 13 } { x - 2 }x−22x3−3x2+x−13​

Solve: 13−32x=3x2\frac { 1 } { 3 } - \frac { 3 } { 2 x } = \frac { 3 } { x ^ { 2 } }31​−2x3​=x23​

Perform the operations and simplify the result when possible. 1+x−xx−31 + x - \frac { x } { x - 3 }1+x−x−3x​

Use the factor theorem and determine whether the first expression is a factor of P ( x ). x+2;P(x)=4x2+8x+3x + 2 ; P ( x ) = 4 x ^ { 2 } + 8 x + 3x+2;P(x)=4x2+8x+3 ( Hint : Write x+2 as x−(−2)x - ( - 2 )x−(−2) .)

Solve the problem by writing a variation model. The distance that a car can go varies directly with the number of gallons of gasoline it consumes. If a car can go 312 miles on 13 gallons of gasoline, how far can it go on a full tank of 18 gallons? __________ mi

Perform the operations and simplify the result when possible. 5x+1−4x−1+x+7x2−1\frac { 5 } { x + 1 } - \frac { 4 } { x - 1 } + \frac { x + 7 } { x ^ { 2 } - 1 }x+15​−x−14​+x2−1x+7​

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

Perform the division. $\frac { 38 x ^ { 5 } y ^ { 6 } - 19 x ^ { 4 } y ^ { 11 } + 57 x y } { 76 x ^ { 2 } y ^ { 4 } }$

Divide: $\frac { 1.2 x ^ { 3 } + 0.1 x ^ { 2 } + 0.2 x - 0.2 } { 0.4 x + 0.3 }$

Perform the indicated operation. Simplify, if possible. $\frac { 2 x ^ { 2 } - 8 } { 10 x ^ { 2 } - 15 x - 10 } \div \frac { x ^ { 2 } + 4 x + 4 } { 4 x + 2 }$

Use synthetic division to perform the division. $\left( m ^ { 3 } - m ^ { 2 } - m - 2 \right) \div ( m + 1 )$

If P ( x ) is a polynomial and if $P ( k ) = 0$ , then k is called a __________ of the polynomial.

Solve the proportion. $\frac { 1 } { x + 2 } = \frac { - 2 x } { x + 3 }$

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

Divide: $\frac { 27 x y ^ { 2 } - 12 x ^ { 3 } y ^ { 5 } } { 9 x ^ { 3 } y ^ { 5 } }$

Perform the division. $\frac { 2 x ^ { 3 } - 3 x ^ { 2 } + x - 13 } { x - 2 }$

Solve: $\frac { 1 } { 3 } - \frac { 3 } { 2 x } = \frac { 3 } { x ^ { 2 } }$

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

Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x + 2 ; P ( x ) = 4 x ^ { 2 } + 8 x + 3$ ( Hint : Write x+2 as $x - ( - 2 )$ .)

Perform the operations and simplify the result when possible. $\frac { 5 } { x + 1 } - \frac { 4 } { x - 1 } + \frac { x + 7 } { x ^ { 2 } - 1 }$