Question 1

Simplify.
-If $P ( x ) = 4 x ^ { 2 } + 4 x + 4$ and $Q ( x ) = 7 x ^ { 2 } - 9$, find $3 [ P ( x ) ] + Q ( x )$.

Accepted Answer

A)  $19 x ^ { 2 } - 12 x + 3$ 
B)  $19 x ^ { 2 } + 12 x - 3$ 
C)  $19 x ^ { 2 } + 12 x + 3$ 
D)  $- 19 x ^ { 2 } + 12 x + 3$ 
A)  $19 x ^ { 2 } - 12 x + 3$ 
B)  $19 x ^ { 2 } + 12 x - 3$ 
C)  $19 x ^ { 2 } + 12 x + 3$ 
D)  $- 19 x ^ { 2 } + 12 x + 3$

Question 2

Evaluate the expression using exponential rules. Write the result in standard notation.
-$\left( 2 \times 10 ^ { - 3 } \right) \left( 5 \times 10 ^ { - 2 } \right)$

Accepted Answer

A)  $0.000001$ 
B)  $0.001$ 
C)  $0.0001$ 
D)  $0.00001$ 
A)  $0.000001$ 
B)  $0.001$ 
C)  $0.0001$ 
D)  $0.00001$

Question 3

Simplify.
-If $P ( x ) = 9 x ^ { 2 } - 1$, find $P ( 0 )$.

Accepted Answer

A)  8 
B)  1 
C)  $- 1$ 
D)  0 
A)  8 
B)  1 
C)  $- 1$ 
D)  0

Question 4

Evaluate the expression.
-$7 \cdot 3 ^ { 3 }$

Accepted Answer

A)  63 
B)  9261 
C)  189 
D)  34 
A)  63 
B)  9261 
C)  189 
D)  34

Question 5

Evaluate the expression.
-$- 3 ^ { 3 }$

Accepted Answer

A)  27 
B)  $- 27$ 
C)  $- 9$ 
D)  9 
A)  27 
B)  $- 27$ 
C)  $- 9$ 
D)  9

Question 6

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of
these.
-$6 y ^ { 4 } + 9 y ^ { 3 } + 3$

Accepted Answer

A)  4; trinomial 
B)  7; trinomial 
C)  8; trinomial 
D)  4; binomial 
A)  4; trinomial 
B)  7; trinomial 
C)  8; trinomial 
D)  4; binomial

Question 7

Use the power rule and the power of a product or quotient rule to simplify the expression.
-$\left( 4 x ^ { 3 } y ^ { 3 } \right) ^ { 2 }$

Accepted Answer

A)  $16 x ^ { 6 } y ^ { 6 }$ 
B)  $4 x ^ { 5 } y ^ { 5 }$ 
C)  $16 x ^ { 5 } y ^ { 5 }$ 
D)  $4 x ^ { 6 } y ^ { 6 }$ 
A)  $16 x ^ { 6 } y ^ { 6 }$ 
B)  $4 x ^ { 5 } y ^ { 5 }$ 
C)  $16 x ^ { 5 } y ^ { 5 }$ 
D)  $4 x ^ { 6 } y ^ { 6 }$

Question 8

Use synthetic division to divide.
-$\left( 2 x ^ { 3 } + 13 x ^ { 2 } + 15 x - 20 \right) \div ( x + 4 )$

Accepted Answer

A)  $- 2 x ^ { 2 } - 4 x - 5$ 
B)  $2 x + 5$ 
C)  $2 x ^ { 2 } + 5 x - 5$ 
D)  $\frac { 1 } { 2 } x ^ { 2 } + \frac { 13 } { 4 } x + \frac { 15 } { 4 }$ 
A)  $- 2 x ^ { 2 } - 4 x - 5$ 
B)  $2 x + 5$ 
C)  $2 x ^ { 2 } + 5 x - 5$ 
D)  $\frac { 1 } { 2 } x ^ { 2 } + \frac { 13 } { 4 } x + \frac { 15 } { 4 }$

Question 9

Multiply.
-$( y - 5 ) ^ { 2 }$

Accepted Answer

A)  $25 y ^ { 2 } - 10 y + 25$ 
B)  $y ^ { 2 } - 10 y + 25$ 
C)  $\mathrm { y } + 25$ 
D)  $\mathrm { y } ^ { 2 } + 25$ 
A)  $25 y ^ { 2 } - 10 y + 25$ 
B)  $y ^ { 2 } - 10 y + 25$ 
C)  $\mathrm { y } + 25$ 
D)  $\mathrm { y } ^ { 2 } + 25$

Question 10

Evaluate the expression.
-$( 0.2 ) ^ { 4 }$

Accepted Answer

A)  $0.16$ 
B)  $0.4096$ 
C)  $0.8$ 
D)  $0.0016$ 
A)  $0.16$ 
B)  $0.4096$ 
C)  $0.8$ 
D)  $0.0016$

Question 11

Multiply.
-$( x + 7 ) ( x - 7 )$

Accepted Answer

A)  $x ^ { 2 } - 14$ 
B)  $x ^ { 2 } + 14 x - 49$ 
C)  $x ^ { 2 } - 14 x - 49$ 
D)  $x ^ { 2 } - 49$ 
A)  $x ^ { 2 } - 14$ 
B)  $x ^ { 2 } + 14 x - 49$ 
C)  $x ^ { 2 } - 14 x - 49$ 
D)  $x ^ { 2 } - 49$

Question 12

Write the number in standard notation.
-$5.57 \times 10 ^ { - 4 }$

Accepted Answer

A)  $0.000557$ 
B)  $0.0000557$ 
C)  $- 557,000$ 
D)  $0.00557$ 
A)  $0.000557$ 
B)  $0.0000557$ 
C)  $- 557,000$ 
D)  $0.00557$

Question 13

Evaluate the expression.
-$- 5 ^ { 3 }$

Accepted Answer

A)  15 
B)  -15 
C)  -125 
D)  125 
A)  15 
B)  -15 
C)  -125 
D)  125

Question 14

Use synthetic division to divide.
-$\left( x ^ { 2 } + 4 x - 5 \right) \div ( x + 6 )$

Accepted Answer

A)  $x - 2$ 
B)  $x - 7 + \frac { 2 } { x + 6 }$ 
C)  $x - 2 + \frac { 7 } { x + 6 }$ 
D)  $x + 2 + \frac { 7 } { x + 6 }$ 
A)  $x - 2$ 
B)  $x - 7 + \frac { 2 } { x + 6 }$ 
C)  $x - 2 + \frac { 7 } { x + 6 }$ 
D)  $x + 2 + \frac { 7 } { x + 6 }$

Question 15

Solve.
-The height of a new building in China will be 987 feet. Neglecting air resistance, the height of an object dropped from this building at time t seconds would be given by the polynomial -16t2 + 987.
Find the height of the object at time t = 3 seconds.

Accepted Answer

A)  939 ft 
B)  843 ft 
C)  891 ft 
D)  1131 ft 
A)  939 ft 
B)  843 ft 
C)  891 ft 
D)  1131 ft

Question 16

Evaluate the expression.
-$6 ^ { 3 }$

Accepted Answer

A)  $- 216$ 
B)  216 
C)  18 
D)  $- 18$ 
A)  $- 216$ 
B)  216 
C)  18 
D)  $- 18$

Question 17

Multiply.
-$( x + 4 ) ^ { 2 }$

Accepted Answer

A)  $x + 16$ 
B)  $16 x ^ { 2 } + 8 x + 16$ 
C)  $x ^ { 2 } + 8 x + 16$ 
D)  $x ^ { 2 } + 16$ 
A)  $x + 16$ 
B)  $16 x ^ { 2 } + 8 x + 16$ 
C)  $x ^ { 2 } + 8 x + 16$ 
D)  $x ^ { 2 } + 16$

Question 18

Multiply.
-$( 4 x + 12 ) ( x + 12 )$

Accepted Answer

A)  $4 x ^ { 2 } + 59 x + 144$ 
B)  $x ^ { 2 } + 60 x + 59$ 
C)  $4 x ^ { 2 } + 60 x + 144$ 
D)  $x ^ { 2 } + 144 x + 60$ 
A)  $4 x ^ { 2 } + 59 x + 144$ 
B)  $x ^ { 2 } + 60 x + 59$ 
C)  $4 x ^ { 2 } + 60 x + 144$ 
D)  $x ^ { 2 } + 144 x + 60$

Question 19

Fill in the blank with one of the words or phrases listed below.

-A polynomial with exactly 3 terms is called a_______

Accepted Answer

A)  monomial 
B)  FOIL 
C)  binomial 
D)  trinomial 
A)  monomial 
B)  FOIL 
C)  binomial 
D)  trinomial

Question 20

Multiply.
-$( x - 3 ) ^ { 3 }$

Accepted Answer

A)  $x ^ { 3 } - 9 x ^ { 2 } + 15 x - 27$ 
B)  $x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$ 
C)  $x ^ { 3 } - 3 x ^ { 2 } + 15 x - 27$ 
D)  $x ^ { 3 } - 9 x ^ { 2 } + 9 x - 27$ 
A)  $x ^ { 3 } - 9 x ^ { 2 } + 15 x - 27$ 
B)  $x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$ 
C)  $x ^ { 3 } - 3 x ^ { 2 } + 15 x - 27$ 
D)  $x ^ { 3 } - 9 x ^ { 2 } + 9 x - 27$

Simplify. -If $P ( x ) = 4 x ^ { 2 } + 4 x + 4$ and $Q ( x ) = 7 x ^ { 2 } - 9$ , find $3 [ P ( x ) ] + Q ( x )$ .

Evaluate the expression using exponential rules. Write the result in standard notation. - $\left( 2 \times 10 ^ { - 3 } \right) \left( 5 \times 10 ^ { - 2 } \right)$

Simplify. -If $P ( x ) = 9 x ^ { 2 } - 1$ , find $P ( 0 )$ .

Evaluate the expression. - $7 \cdot 3 ^ { 3 }$

Evaluate the expression. - $- 3 ^ { 3 }$

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $6 y ^ { 4 } + 9 y ^ { 3 } + 3$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $\left( 4 x ^ { 3 } y ^ { 3 } \right) ^ { 2 }$

Use synthetic division to divide. - $\left( 2 x ^ { 3 } + 13 x ^ { 2 } + 15 x - 20 \right) \div ( x + 4 )$

Multiply. - $( y - 5 ) ^ { 2 }$

Evaluate the expression. - $( 0.2 ) ^ { 4 }$

Multiply. - $( x + 7 ) ( x - 7 )$

Write the number in standard notation. - $5.57 \times 10 ^ { - 4 }$

Evaluate the expression. - $- 5 ^ { 3 }$

Use synthetic division to divide. - $\left( x ^ { 2 } + 4 x - 5 \right) \div ( x + 6 )$

Solve. -The height of a new building in China will be 987 feet. Neglecting air resistance, the height of an object dropped from this building at time t seconds would be given by the polynomial -16t2 + 987. Find the height of the object at time t = 3 seconds.

Evaluate the expression. - $6 ^ { 3 }$

Multiply. - $( x + 4 ) ^ { 2 }$

Multiply. - $( 4 x + 12 ) ( x + 12 )$

Fill in the blank with one of the words or phrases listed below. -A polynomial with exactly 3 terms is called a_______

Multiply. - $( x - 3 ) ^ { 3 }$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

Simplify. -If P(x)=4x2+4x+4P ( x ) = 4 x ^ { 2 } + 4 x + 4P(x)=4x2+4x+4 and Q(x)=7x2−9Q ( x ) = 7 x ^ { 2 } - 9Q(x)=7x2−9 , find 3[P(x)]+Q(x)3 [ P ( x ) ] + Q ( x )3[P(x)]+Q(x) .

Evaluate the expression using exponential rules. Write the result in standard notation. - (2×10−3)(5×10−2)\left( 2 \times 10 ^ { - 3 } \right) \left( 5 \times 10 ^ { - 2 } \right)(2×10−3)(5×10−2)

Simplify. -If P(x)=9x2−1P ( x ) = 9 x ^ { 2 } - 1P(x)=9x2−1 , find P(0)P ( 0 )P(0) .

Evaluate the expression. - 7⋅337 \cdot 3 ^ { 3 }7⋅33

Evaluate the expression. - −33- 3 ^ { 3 }−33

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - 6y4+9y3+36 y ^ { 4 } + 9 y ^ { 3 } + 36y4+9y3+3

Use the power rule and the power of a product or quotient rule to simplify the expression. - (4x3y3)2\left( 4 x ^ { 3 } y ^ { 3 } \right) ^ { 2 }(4x3y3)2

Use synthetic division to divide. - (2x3+13x2+15x−20)÷(x+4)\left( 2 x ^ { 3 } + 13 x ^ { 2 } + 15 x - 20 \right) \div ( x + 4 )(2x3+13x2+15x−20)÷(x+4)

Multiply. - (y−5)2( y - 5 ) ^ { 2 }(y−5)2

Evaluate the expression. - (0.2)4( 0.2 ) ^ { 4 }(0.2)4

Multiply. - (x+7)(x−7)( x + 7 ) ( x - 7 )(x+7)(x−7)

Write the number in standard notation. - 5.57×10−45.57 \times 10 ^ { - 4 }5.57×10−4

Evaluate the expression. - −53- 5 ^ { 3 }−53

Use synthetic division to divide. - (x2+4x−5)÷(x+6)\left( x ^ { 2 } + 4 x - 5 \right) \div ( x + 6 )(x2+4x−5)÷(x+6)