Question 1

Evaluate the polynomial or polynomial function for the given value of the variable.
-$2 x ^ { 2 } + 5 x - 7$ for $x = - 2$

Accepted Answer

A)  $- 21$ 
B)  $- 19$ 
C)  $- 13$ 
D)  $- 9$ 
A)  $- 21$ 
B)  $- 19$ 
C)  $- 13$ 
D)  $- 9$ D

Question 2

Perform the indicated calculation. Express your answer using scientific notation.
-$$\left( 15.64 \times 10 ^ { 3 } \right) \div \left( 4 \times 10 ^ { - 5 } \right)$$

Accepted Answer

A)  $7.82 \times 10 ^ { - 2 }$ 
B)  $7.82 \times 10 ^ { 8 }$ 
C)  $3.91 \times 10 ^ { 8 }$ 
D)  $3.91 \times 10 ^ { - 2 }$ 
A)  $7.82 \times 10 ^ { - 2 }$ 
B)  $7.82 \times 10 ^ { 8 }$ 
C)  $3.91 \times 10 ^ { 8 }$ 
D)  $3.91 \times 10 ^ { - 2 }$ C

Question 3

Convert the given number to scientific notation.
-0.000571

Accepted Answer

A)  $5.71 \times 10 ^ { - 5 }$ 
B)  $5.71 \times 10 ^ { - 4 }$ 
C)  $5.71 \times 10 ^ { - 3 }$ 
D)  $5.71 \times 10 ^ { 4 }$ 
A)  $5.71 \times 10 ^ { - 5 }$ 
B)  $5.71 \times 10 ^ { - 4 }$ 
C)  $5.71 \times 10 ^ { - 3 }$ 
D)  $5.71 \times 10 ^ { 4 }$ B

Question 4

Simplify. (Assume all variables are nonzero.)
-$\frac { x ^ { 6 } } { x ^ { 4 } }$

Accepted Answer

A)  $x ^ { 2 }$ 
B)  $x ^ { 10 }$ 
C)  $x ^ { 1.5 }$ 
D)  $1.5$ 
A)  $x ^ { 2 }$ 
B)  $x ^ { 10 }$ 
C)  $x ^ { 1.5 }$ 
D)  $1.5$

Question 5

Evaluate the polynomial or polynomial function for the given value of the variable.
-$4 x ^ { 3 } - 4 x ^ { 2 } + 5$ for $x = 2$

Accepted Answer

A)  11 
B)  21 
C)  29 
D)  9 
A)  11 
B)  21 
C)  29 
D)  9

Question 6

Add or subtract.
-$\left( 9 m ^ { 2 } n - 2 m n + 4 m n ^ { 2 } \right) - \left( 5 m ^ { 2 } n + 2 m n - 6 m n ^ { 2 } \right)$

Accepted Answer

A)  $4 m ^ { 4 } n ^ { 2 } - 4 m ^ { 2 } n ^ { 2 } + 10 m ^ { 2 } n ^ { 4 }$ 
B)  $4 m ^ { 2 } n - 4 m n + 10 m n ^ { 2 }$ 
C)  $4 m ^ { 2 } n + 6$ 
D)  $4 m ^ { 4 } n ^ { 2 } - 4 m n + 10 m ^ { 2 } n ^ { 4 }$ 
A)  $4 m ^ { 4 } n ^ { 2 } - 4 m ^ { 2 } n ^ { 2 } + 10 m ^ { 2 } n ^ { 4 }$ 
B)  $4 m ^ { 2 } n - 4 m n + 10 m n ^ { 2 }$ 
C)  $4 m ^ { 2 } n + 6$ 
D)  $4 m ^ { 4 } n ^ { 2 } - 4 m n + 10 m ^ { 2 } n ^ { 4 }$

Question 7

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero
real numbers.)
-$$\left( a ^ { - 3 } \right) ^ { - 5 }$$

Accepted Answer

A)  $\frac { 1 } { a ^ { 15 } }$ 
B)  $\frac { 1 } { a ^ { 2 } }$ 
C)  $a ^ { 2 }$ 
D)  $\mathrm { a }^{ 15}$ 
A)  $\frac { 1 } { a ^ { 15 } }$ 
B)  $\frac { 1 } { a ^ { 2 } }$ 
C)  $a ^ { 2 }$ 
D)  $\mathrm { a }^{ 15}$

Question 8

Simplify.
-$\mathrm { m } ^ { 14}\cdot \mathrm { m } ^ { 20 }$

Accepted Answer

A)  $\mathrm { m } ^ { 6 }$ 
B)  $m ^ { 34 }$ 
C)  $\mathrm { m } ^ { 280 }$ 
D)  $34 \mathrm {~m}$ 
A)  $\mathrm { m } ^ { 6 }$ 
B)  $m ^ { 34 }$ 
C)  $\mathrm { m } ^ { 280 }$ 
D)  $34 \mathrm {~m}$

Question 9

Perform the indicated calculation. Express your answer using scientific notation.
-$$( 6,350,000,000 ) \div ( 2,318,000 )$$

Accepted Answer

A)  $2.74 \times 10 ^ { - 3 }$ 
B)  $2.74 \times 10 ^ { 3 }$ 
C)  $2.74 \times 10 ^ { 4 }$ 
D)  $2.74 \times 10^6$ 
A)  $2.74 \times 10 ^ { - 3 }$ 
B)  $2.74 \times 10 ^ { 3 }$ 
C)  $2.74 \times 10 ^ { 4 }$ 
D)  $2.74 \times 10^6$

Question 10

Evaluate the polynomial.
-$b ^ { 2 } - 4 a c$ for $a = 5 , b = - 2$ and $c = 2$

Accepted Answer

A)  $- 32$ 
B)  $- 36$ 
C)  $- 42$ 
D)  $- 46$ 
A)  $- 32$ 
B)  $- 36$ 
C)  $- 42$ 
D)  $- 46$

Question 11

Divide using long division.
-$\frac { 5 x ^ { 2 } + 29 x + 12 } { x + 5 }$

Accepted Answer

A)  $5 x + 4 - \frac { 8 } { x + 5 }$ 
B)  $5 x - 4 - \frac { 8 } { x + 5 }$ 
C)  $5 x + 4 + \frac { 8 } { x + 5 }$ 
D)  $5 x + 4$ 
A)  $5 x + 4 - \frac { 8 } { x + 5 }$ 
B)  $5 x - 4 - \frac { 8 } { x + 5 }$ 
C)  $5 x + 4 + \frac { 8 } { x + 5 }$ 
D)  $5 x + 4$

Question 12

Solve the problem. Express your answer in scientific notation, and round to one decimal place.
-In a state with a population of 7,000,000 people, the average citizen spends $6,000 on housing each year. What is the total spent on housing for the state?

Accepted Answer

A)  $\$ 4.2 \times 10 ^ { 10 }$ 
B)  $\$ 4.2 \times 10 ^ { 9 }$ 
C)  $\$ 42 \times 10^{10}$ 
D)  $\$ 42 \times 10 ^ { 11 }$ 
A)  $\$ 4.2 \times 10 ^ { 10 }$ 
B)  $\$ 4.2 \times 10 ^ { 9 }$ 
C)  $\$ 42 \times 10^{10}$ 
D)  $\$ 42 \times 10 ^ { 11 }$

Question 13

Solve the problem. Round your answer to the nearest whole number, if necessary.
-The distance in feet it takes a car traveling at x mph to come to a full stop after hitting the brakes is given by the function $$f ( x ) = 1.27 x ^ { 2 } + 0.063 x$$

Accepted Answer

A)  1145 feet 
B)  1161 feet 
C)  1137 feet 
D)  1 feet 
A)  1145 feet 
B)  1161 feet 
C)  1137 feet 
D)  1 feet

Question 14

Find the special product using the appropriate formula.
-$$( 6 x - 5 ) ^ { 2 }$$

Accepted Answer

A)  $36 x ^ { 2 } - 60 x + 25$ 
B)  $6 x ^ { 2 } - 60 x + 25$ 
C)  $36 x ^ { 2 } + 25$ 
D)  $6 x ^ { 2 } + 25$ 
A)  $36 x ^ { 2 } - 60 x + 25$ 
B)  $6 x ^ { 2 } - 60 x + 25$ 
C)  $36 x ^ { 2 } + 25$ 
D)  $6 x ^ { 2 } + 25$

Question 15

Evaluate the polynomial or polynomial function for the given value of the variable.
-$$f ( x ) = 2 x ^ { 5 } - 2 x ^ { 4 } + 5 x ^ { 3 } - x ^ { 2 } , f ( 2 )$$

Accepted Answer

A)  97 
B)  64 
C)  63 
D)  68 
A)  97 
B)  64 
C)  63 
D)  68

Question 16

Find the missing dividend or divisor.
-$$\frac { 6 x ^ { 2 } + 10 x - 4 } { ? } = 3 x - 1$$

Accepted Answer

A)  $x - 4$ 
B)  $2 x - 4$ 
C)  $2 x + 4$ 
D)  $x + 4$ 
A)  $x - 4$ 
B)  $2 x - 4$ 
C)  $2 x + 4$ 
D)  $x + 4$

Question 17

Convert the given number to scientific notation.
-83,000,000

Accepted Answer

A)  $8.3 \times 10 ^ { 6 }$ 
B)  $8.3 \times 10 ^ { - 7 }$ 
C)  $8.3 \times 10 ^ { - 6 }$ 
D)  $8.3 \times 10 ^ { 7 }$ 
A)  $8.3 \times 10 ^ { 6 }$ 
B)  $8.3 \times 10 ^ { - 7 }$ 
C)  $8.3 \times 10 ^ { - 6 }$ 
D)  $8.3 \times 10 ^ { 7 }$

Question 18

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero
real numbers.)
-$\frac { x ^ { - 2 } } { x ^ { - 7 } }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 5 } }$ 
B)  $x ^ { 5 }$ 
C)  $x ^ { 9 }$ 
D)  $\frac { 1 } { x ^ { 9 } }$ 
A)  $\frac { 1 } { x ^ { 5 } }$ 
B)  $x ^ { 5 }$ 
C)  $x ^ { 9 }$ 
D)  $\frac { 1 } { x ^ { 9 } }$

Question 19

Find the missing factor or exponent(s).
-$$( x ? y ? ) ^ { 6 } = x ^ { 60 } y ^{72}$$

Accepted Answer

A)  54,66 
B)  6,12 
C)  10,12 
D)  10,6 
A)  54,66 
B)  6,12 
C)  10,12 
D)  10,6

Question 20

Perform the indicated calculation. Express your answer using scientific notation.
-$\left( 15 \times 10 ^ { - 5 } \right) \div \left( 3 \times 10 ^ { 4 } \right)$

Accepted Answer

A)  $10 \times 10 ^ { - 9 }$ 
B)  $5 \times 10 ^ { - 1 }$ 
C)  $5 \times 10 ^ { - 9 }$ 
D)  $10 \times 10 ^ { - 1 }$ 
A)  $10 \times 10 ^ { - 9 }$ 
B)  $5 \times 10 ^ { - 1 }$ 
C)  $5 \times 10 ^ { - 9 }$ 
D)  $10 \times 10 ^ { - 1 }$

Evaluate the polynomial or polynomial function for the given value of the variable. - $2 x ^ { 2 } + 5 x - 7$ for $x = - 2$

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 15.64 \times 10 ^ { 3 } \right) \div \left( 4 \times 10 ^ { - 5 } \right)$

Convert the given number to scientific notation. -0.000571

Simplify. (Assume all variables are nonzero.) - $\frac { x ^ { 6 } } { x ^ { 4 } }$

Evaluate the polynomial or polynomial function for the given value of the variable. - $4 x ^ { 3 } - 4 x ^ { 2 } + 5$ for $x = 2$

Add or subtract. - $\left( 9 m ^ { 2 } n - 2 m n + 4 m n ^ { 2 } \right) - \left( 5 m ^ { 2 } n + 2 m n - 6 m n ^ { 2 } \right)$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left( a ^ { - 3 } \right) ^ { - 5 }$

Simplify. - $\mathrm { m } ^ { 14}\cdot \mathrm { m } ^ { 20 }$

Perform the indicated calculation. Express your answer using scientific notation. - $( 6,350,000,000 ) \div ( 2,318,000 )$

Evaluate the polynomial. - $b ^ { 2 } - 4 a c$ for $a = 5 , b = - 2$ and $c = 2$

Divide using long division. - $\frac { 5 x ^ { 2 } + 29 x + 12 } { x + 5 }$

Solve the problem. Express your answer in scientific notation, and round to one decimal place. -In a state with a population of 7,000,000 people, the average citizen spends $6,000 on housing each year. What is the total spent on housing for the state?

Solve the problem. Round your answer to the nearest whole number, if necessary. -The distance in feet it takes a car traveling at x mph to come to a full stop after hitting the brakes is given by the function $f ( x ) = 1.27 x ^ { 2 } + 0.063 x$

Find the special product using the appropriate formula. - $( 6 x - 5 ) ^ { 2 }$

Evaluate the polynomial or polynomial function for the given value of the variable. - $f ( x ) = 2 x ^ { 5 } - 2 x ^ { 4 } + 5 x ^ { 3 } - x ^ { 2 } , f ( 2 )$

Find the missing dividend or divisor. - $\frac { 6 x ^ { 2 } + 10 x - 4 } { ? } = 3 x - 1$

Convert the given number to scientific notation. -83,000,000

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac { x ^ { - 2 } } { x ^ { - 7 } }$

Find the missing factor or exponent(s). - $( x ? y ? ) ^ { 6 } = x ^ { 60 } y ^{72}$

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 15 \times 10 ^ { - 5 } \right) \div \left( 3 \times 10 ^ { 4 } \right)$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

Evaluate the polynomial or polynomial function for the given value of the variable. - 2x2+5x−72 x ^ { 2 } + 5 x - 72x2+5x−7 for x=−2x = - 2x=−2

Perform the indicated calculation. Express your answer using scientific notation. - (15.64×103)÷(4×10−5)\left( 15.64 \times 10 ^ { 3 } \right) \div \left( 4 \times 10 ^ { - 5 } \right)(15.64×103)÷(4×10−5)

Convert the given number to scientific notation. -0.000571

Simplify. (Assume all variables are nonzero.) - x6x4\frac { x ^ { 6 } } { x ^ { 4 } }x4x6​

Evaluate the polynomial or polynomial function for the given value of the variable. - 4x3−4x2+54 x ^ { 3 } - 4 x ^ { 2 } + 54x3−4x2+5 for x=2x = 2x=2

Add or subtract. - (9m2n−2mn+4mn2)−(5m2n+2mn−6mn2)\left( 9 m ^ { 2 } n - 2 m n + 4 m n ^ { 2 } \right) - \left( 5 m ^ { 2 } n + 2 m n - 6 m n ^ { 2 } \right)(9m2n−2mn+4mn2)−(5m2n+2mn−6mn2)

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - (a−3)−5\left( a ^ { - 3 } \right) ^ { - 5 }(a−3)−5

Simplify. - m14⋅m20\mathrm { m } ^ { 14}\cdot \mathrm { m } ^ { 20 }m14⋅m20

Perform the indicated calculation. Express your answer using scientific notation. - (6,350,000,000)÷(2,318,000)( 6,350,000,000 ) \div ( 2,318,000 )(6,350,000,000)÷(2,318,000)

Evaluate the polynomial. - b2−4acb ^ { 2 } - 4 a cb2−4ac for a=5,b=−2a = 5 , b = - 2a=5,b=−2 and c=2c = 2c=2

Divide using long division. - 5x2+29x+12x+5\frac { 5 x ^ { 2 } + 29 x + 12 } { x + 5 }x+55x2+29x+12​