Question 1

Multiply.
-$$2 x ( - 10 x + 2 )$$

Accepted Answer

A)  $- 10 x ^ { 2 } + 4 x$ 
B)  $- 20 x ^ { 2 } + 2 x$ 
C)  $- 20 x ^ { 2 } + 4 x$ 
D)  $- 16 x ^ { 2 }$ 
A)  $- 10 x ^ { 2 } + 4 x$ 
B)  $- 20 x ^ { 2 } + 2 x$ 
C)  $- 20 x ^ { 2 } + 4 x$ 
D)  $- 16 x ^ { 2 }$

Question 2

Find the special product using the appropriate formula.
-$$( x + 12 ) ( x - 12 )$$

Accepted Answer

A)  $x ^ { 2 } - 144$ 
B)  $x ^ { 2 } - 24 x - 144$ 
C)  $x ^ { 2 } - 24$ 
D)  $x ^ { 2 } + 24 x - 144$ 
A)  $x ^ { 2 } - 144$ 
B)  $x ^ { 2 } - 24 x - 144$ 
C)  $x ^ { 2 } - 24$ 
D)  $x ^ { 2 } + 24 x - 144$

Question 3

Evaluate the polynomial or polynomial function for the given value of the variable.
-$$f ( x ) = - 3 x ^ { 3 } + 6 x ^ { 2 } + 9 x + 1 , f ( - 1 )$$

Accepted Answer

A)  19 
B)  13 
C)  1 
D)  $- 13$ 
A)  19 
B)  13 
C)  1 
D)  $- 13$

Question 4

Evaluate the given function.
-$$f ( x ) = x ^ { 3 } , f ( - 5 )$$

Accepted Answer

A)  $- 5 x ^ { 3 }$ 
B)  $x ^ { - 15 }$ 
C)  $- 125$ 
D)  -15 
A)  $- 5 x ^ { 3 }$ 
B)  $x ^ { - 15 }$ 
C)  $- 125$ 
D)  -15

Question 5

Add or subtract.
-$\left( 6 x ^ { 2 } y - 4 x y + 4 x y ^ { 2 } \right) - \left( 6 x y - 4 x y ^ { 2 } + 3 x ^ { 2 } y \right)$

Accepted Answer

A)  $7 x ^ { 2 } y + 4 x y ^ { 2 } - 10 x y$ 
B)  $3 x ^ { 2 } y - 8 x y ^ { 2 } + 2 x y$ 
C)  $3 x ^ { 2 } y + 8 x y ^ { 2 } - 10 x y$ 
D)  $3 x ^ { 2 } y - 8 x y ^ { 2 } - 10 x y$ 
A)  $7 x ^ { 2 } y + 4 x y ^ { 2 } - 10 x y$ 
B)  $3 x ^ { 2 } y - 8 x y ^ { 2 } + 2 x y$ 
C)  $3 x ^ { 2 } y + 8 x y ^ { 2 } - 10 x y$ 
D)  $3 x ^ { 2 } y - 8 x y ^ { 2 } - 10 x y$

Question 6

Add or subtract.
-$$\left( 2 x ^ { 6 } + 2 x ^ { 5 } + 4 x ^ { 4 } + 6 \right) - \left( 5 x ^ { 6 } - 8 x ^ { 5 } + 7 x ^ { 4 } + 3 \right)$$

Accepted Answer

A)  $- 3 x ^ { 6 } + 10 x ^ { 5 } - 3 x ^ { 4 } + 3$ 
B)  $7 x ^ { 6 } - 6 x ^ { 5 } + 11 x ^ { 4 } + 9$ 
C)  $- 3 x ^ { 6 } + 6 x ^ { 5 } - 11 x ^ { 4 } + 9$ 
D)  $7 x ^ { 6 } - 6 x ^ { 5 } + 11 x ^ { 4 } + 3$ 
A)  $- 3 x ^ { 6 } + 10 x ^ { 5 } - 3 x ^ { 4 } + 3$ 
B)  $7 x ^ { 6 } - 6 x ^ { 5 } + 11 x ^ { 4 } + 9$ 
C)  $- 3 x ^ { 6 } + 6 x ^ { 5 } - 11 x ^ { 4 } + 9$ 
D)  $7 x ^ { 6 } - 6 x ^ { 5 } + 11 x ^ { 4 } + 3$

Question 7

Find the missing monomial, factor or term.
-$$( 8 x + 1 ) \cdot ? = 64 x ^ { 2 } - 1$$

Accepted Answer

A)  $8 x + 8$ 
B)  $x - 1$ 
C)  $8 x - 1$ 
D)  $8 x + 1$ 
A)  $8 x + 8$ 
B)  $x - 1$ 
C)  $8 x - 1$ 
D)  $8 x + 1$

Question 8

Solve the problem. Round your answer to the nearest whole number, if necessary.
-The distance an object moves in a straight line (in meters) is given by the function $$f ( t ) = 6 t ^ { 2 } - 3 t$$

Accepted Answer

A)  675 meters 
B)  45 meters 
C)  585 meters 
D)  1305 meters 
A)  675 meters 
B)  45 meters 
C)  585 meters 
D)  1305 meters

Question 9

Simplify.
-$$\left( 10 x ^ { 3 } \right) ^ { 3 }$$

Accepted Answer

A)  $10 x ^ { 3 }$ 
B)  $10 x ^ { 9 }$ 
C)  $1000 x ^ { 9 }$ 
D)  $1000 x ^ { 27 }$ 
A)  $10 x ^ { 3 }$ 
B)  $10 x ^ { 9 }$ 
C)  $1000 x ^ { 9 }$ 
D)  $1000 x ^ { 27 }$

Question 10

Find the missing monomial, factor or term.
-$$- 3 x ^ { 4 } ( ? ) = 33 x ^ { 9 } - 15 x ^ { 7 } - 9 x ^ { 4 }$$

Accepted Answer

A)  $- 11 x ^ { 5 } + 5 x ^ { 3 } - 3$ 
B)  $- 11 x ^ { 5 } + 5 x ^ { 3 } + 3 x$ 
C)  $- 11 x ^ { 5 } + 5 x ^ { 3 } + 3$ 
D)  $- 11 x ^ { 5 } - 5 x ^ { 3 } + 3$ 
A)  $- 11 x ^ { 5 } + 5 x ^ { 3 } - 3$ 
B)  $- 11 x ^ { 5 } + 5 x ^ { 3 } + 3 x$ 
C)  $- 11 x ^ { 5 } + 5 x ^ { 3 } + 3$ 
D)  $- 11 x ^ { 5 } - 5 x ^ { 3 } + 3$

Question 11

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero
real numbers.)
-$\frac { z ^ { - 7 } } { z ^ { - 5 } }$

Accepted Answer

A)  $\frac { 1 } { z ^ { 2 } }$ 
B)  $\frac { 1 } { z ^ { - 2 } }$ 
C)  $z ^ { 2 }$ 
D)  $\mathrm { z } ^ { 12 }$ 
A)  $\frac { 1 } { z ^ { 2 } }$ 
B)  $\frac { 1 } { z ^ { - 2 } }$ 
C)  $z ^ { 2 }$ 
D)  $\mathrm { z } ^ { 12 }$

Question 12

-$\left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { 2 a } { 2 b }$ 
B)  2 
C)  $\frac { a ^ { 2 } } { b ^ { 2 } }$ 
D)  $\frac { a ^ { 2 } } { b }$ 
A)  $\frac { 2 a } { 2 b }$ 
B)  2 
C)  $\frac { a ^ { 2 } } { b ^ { 2 } }$ 
D)  $\frac { a ^ { 2 } } { b }$

Question 13

Convert the given number to scientific notation.
-0.000009447

Accepted Answer

A)  $9.447 \times 10 ^ { - 5 }$ 
B)  $9.447 \times 10 ^ { - 7 }$ 
C)  $9.447 \times 10 ^ { - 6 }$ 
D)  $9.447 \times 10 ^ { 6 }$ 
A)  $9.447 \times 10 ^ { - 5 }$ 
B)  $9.447 \times 10 ^ { - 7 }$ 
C)  $9.447 \times 10 ^ { - 6 }$ 
D)  $9.447 \times 10 ^ { 6 }$

Question 14

Simplify. (Assume all variables are nonzero.)
-$\mathrm { z } ^ { 35 } \div \mathrm { z } ^ { 5 }$

Accepted Answer

A)  $z ^ { 40 }$ 
B)  $\mathrm { z } ^ { 7 }$ 
C)  $\mathrm { z } ^ { 30 }$ 
D)  $\mathrm { z }^{ 175}$ 
A)  $z ^ { 40 }$ 
B)  $\mathrm { z } ^ { 7 }$ 
C)  $\mathrm { z } ^ { 30 }$ 
D)  $\mathrm { z }^{ 175}$

Question 15

Evaluate the polynomial or polynomial function for the given value of the variable.
-$x ^ { 2 } - 5 x - 6$ for $x = - 1$

Accepted Answer

A)  0 
B)  $- 10$ 
C)  12 
D)  2 
A)  0 
B)  $- 10$ 
C)  12 
D)  2

Question 16

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$x^{-6}$

Accepted Answer

A)  $x ^ { 6 }$ 
B)  $6 x$ 
C)  $\frac { 1 } { x ^ { - 6 } }$ 
D)  $\frac { 1 } { x ^ { 6 } }$ 
A)  $x ^ { 6 }$ 
B)  $6 x$ 
C)  $\frac { 1 } { x ^ { - 6 } }$ 
D)  $\frac { 1 } { x ^ { 6 } }$

Question 17

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$3 x ^ { - 6 }$

Accepted Answer

A)  $- 3 x$ 
B)  $\frac { 3 } { x ^ { 6 } }$ 
C)  $3 x ^ { 6 }$ 
D)  $\frac { 1 } { 3 x ^ { 6 } }$ 
A)  $- 3 x$ 
B)  $\frac { 3 } { x ^ { 6 } }$ 
C)  $3 x ^ { 6 }$ 
D)  $\frac { 1 } { 3 x ^ { 6 } }$

Question 18

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero
real numbers.)
-$y ^ { - 6 } \cdot y ^ { - 2 }$

Accepted Answer

A)  $\frac { 1 } { y ^ { - 8 } }$ 
B)  $\frac { 1 } { \mathrm { y } ^ { 4 } }$ 
C)  $y ^ { 8 }$ 
D)  $\frac { 1 } { y ^ { 8 } }$ 
A)  $\frac { 1 } { y ^ { - 8 } }$ 
B)  $\frac { 1 } { \mathrm { y } ^ { 4 } }$ 
C)  $y ^ { 8 }$ 
D)  $\frac { 1 } { y ^ { 8 } }$

Question 19

Evaluate the given function.
-$$g ( x ) = x ^ { 5 } , g ( 6 )$$

Accepted Answer

A)  $x ^ { 30 }$ 
B)  30 
C)  $6 x ^ { 5 }$ 
D)  7776 
A)  $x ^ { 30 }$ 
B)  30 
C)  $6 x ^ { 5 }$ 
D)  7776

Question 20

Simplify. (Assume all variables are nonzero.)
-$$\frac { ( 5 x - 11 ) ^ { 10 } } { ( 5 x - 11 ) ^ { 4 } }$$

Accepted Answer

A)  1 
B)  $( 5 x - 11 ) ^ { 40 }$ 
C)  $( 5 x - 11 ) ^ { 6 }$ 
D)  $( 5 x - 11 ) ^ { 14 }$ 
A)  1 
B)  $( 5 x - 11 ) ^ { 40 }$ 
C)  $( 5 x - 11 ) ^ { 6 }$ 
D)  $( 5 x - 11 ) ^ { 14 }$

Multiply. - $2 x ( - 10 x + 2 )$

Find the special product using the appropriate formula. - $( x + 12 ) ( x - 12 )$

Evaluate the polynomial or polynomial function for the given value of the variable. - $f ( x ) = - 3 x ^ { 3 } + 6 x ^ { 2 } + 9 x + 1 , f ( - 1 )$

Evaluate the given function. - $f ( x ) = x ^ { 3 } , f ( - 5 )$

Add or subtract. - $\left( 6 x ^ { 2 } y - 4 x y + 4 x y ^ { 2 } \right) - \left( 6 x y - 4 x y ^ { 2 } + 3 x ^ { 2 } y \right)$

Add or subtract. - $\left( 2 x ^ { 6 } + 2 x ^ { 5 } + 4 x ^ { 4 } + 6 \right) - \left( 5 x ^ { 6 } - 8 x ^ { 5 } + 7 x ^ { 4 } + 3 \right)$

Find the missing monomial, factor or term. - $( 8 x + 1 ) \cdot ? = 64 x ^ { 2 } - 1$

Solve the problem. Round your answer to the nearest whole number, if necessary. -The distance an object moves in a straight line (in meters) is given by the function $f ( t ) = 6 t ^ { 2 } - 3 t$

Simplify. - $\left( 10 x ^ { 3 } \right) ^ { 3 }$

Find the missing monomial, factor or term. - $- 3 x ^ { 4 } ( ? ) = 33 x ^ { 9 } - 15 x ^ { 7 } - 9 x ^ { 4 }$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac { z ^ { - 7 } } { z ^ { - 5 } }$

$- \left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { 2 }$ $- \left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { 2 }$ - $\left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { 2 }$

Convert the given number to scientific notation. -0.000009447

Simplify. (Assume all variables are nonzero.) - $\mathrm { z } ^ { 35 } \div \mathrm { z } ^ { 5 }$

Evaluate the polynomial or polynomial function for the given value of the variable. - $x ^ { 2 } - 5 x - 6$ for $x = - 1$

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - $x^{-6}$

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - $3 x ^ { - 6 }$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $y ^ { - 6 } \cdot y ^ { - 2 }$

Evaluate the given function. - $g ( x ) = x ^ { 5 } , g ( 6 )$

Simplify. (Assume all variables are nonzero.) - $\frac { ( 5 x - 11 ) ^ { 10 } } { ( 5 x - 11 ) ^ { 4 } }$

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

Multiply. - 2x(−10x+2)2 x ( - 10 x + 2 )2x(−10x+2)

Find the special product using the appropriate formula. - (x+12)(x−12)( x + 12 ) ( x - 12 )(x+12)(x−12)

Evaluate the polynomial or polynomial function for the given value of the variable. - f(x)=−3x3+6x2+9x+1,f(−1)f ( x ) = - 3 x ^ { 3 } + 6 x ^ { 2 } + 9 x + 1 , f ( - 1 )f(x)=−3x3+6x2+9x+1,f(−1)

Evaluate the given function. - f(x)=x3,f(−5)f ( x ) = x ^ { 3 } , f ( - 5 )f(x)=x3,f(−5)

Add or subtract. - (6x2y−4xy+4xy2)−(6xy−4xy2+3x2y)\left( 6 x ^ { 2 } y - 4 x y + 4 x y ^ { 2 } \right) - \left( 6 x y - 4 x y ^ { 2 } + 3 x ^ { 2 } y \right)(6x2y−4xy+4xy2)−(6xy−4xy2+3x2y)

Add or subtract. - (2x6+2x5+4x4+6)−(5x6−8x5+7x4+3)\left( 2 x ^ { 6 } + 2 x ^ { 5 } + 4 x ^ { 4 } + 6 \right) - \left( 5 x ^ { 6 } - 8 x ^ { 5 } + 7 x ^ { 4 } + 3 \right)(2x6+2x5+4x4+6)−(5x6−8x5+7x4+3)

Find the missing monomial, factor or term. - (8x+1)⋅?=64x2−1( 8 x + 1 ) \cdot ? = 64 x ^ { 2 } - 1(8x+1)⋅?=64x2−1

Solve the problem. Round your answer to the nearest whole number, if necessary. -The distance an object moves in a straight line (in meters) is given by the function f(t)=6t2−3tf ( t ) = 6 t ^ { 2 } - 3 tf(t)=6t2−3t

Simplify. - (10x3)3\left( 10 x ^ { 3 } \right) ^ { 3 }(10x3)3

Find the missing monomial, factor or term. - −3x4(?)=33x9−15x7−9x4- 3 x ^ { 4 } ( ? ) = 33 x ^ { 9 } - 15 x ^ { 7 } - 9 x ^ { 4 }−3x4(?)=33x9−15x7−9x4

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - z−7z−5\frac { z ^ { - 7 } } { z ^ { - 5 } }z−5z−7​

- (ab)2\left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { 2 }(ba​)2