Question 1

Multiply.
-$( 2 a - 1 ) ^ { 2 }$

Accepted Answer

A)  $4 a ^ { 2 } - 4 a + 1$ 
B)  $2 a ^ { 2 } - 4 a + 1$ 
C)  $4 a ^ { 2 } + 1$ 
D)  $2 a ^ { 2 } + 1$ 
A)  $4 a ^ { 2 } - 4 a + 1$ 
B)  $2 a ^ { 2 } - 4 a + 1$ 
C)  $4 a ^ { 2 } + 1$ 
D)  $2 a ^ { 2 } + 1$

Question 2

Multiply.
-$( 10 z + 7 ) ^ { 2 }$

Accepted Answer

A)  $10 z ^ { 2 } + 49$ 
B)  $100 z ^ { 2 } + 49$ 
C)  $10 z ^ { 2 } + 140 z + 49$ 
D)  $100 z ^ { 2 } + 140 z + 49$ 
A)  $10 z ^ { 2 } + 49$ 
B)  $100 z ^ { 2 } + 49$ 
C)  $10 z ^ { 2 } + 140 z + 49$ 
D)  $100 z ^ { 2 } + 140 z + 49$

Question 3

Multiply.
-$( 8 x - 1 ) \left( x ^ { 2 } - 5 x + 1 \right)$

Accepted Answer

A)  $8 x ^ { 3 } - 39 x ^ { 2 } + 3 x - 1$ 
B)  $8 x ^ { 3 } - 40 x ^ { 2 } + 8 x + 1$ 
C)  $8 x ^ { 3 } - 41 x ^ { 2 } + 13 x - 1$ 
D)  $8 x ^ { 3 } + 41 x ^ { 2 } - 13 x + 1$ 
A)  $8 x ^ { 3 } - 39 x ^ { 2 } + 3 x - 1$ 
B)  $8 x ^ { 3 } - 40 x ^ { 2 } + 8 x + 1$ 
C)  $8 x ^ { 3 } - 41 x ^ { 2 } + 13 x - 1$ 
D)  $8 x ^ { 3 } + 41 x ^ { 2 } - 13 x + 1$

Question 4

Simplify the expression. Write the result using positive exponents only.
-$\frac { 7 p ^ { - 3 } } { 3 p ^ { 9 } }$

Accepted Answer

A)  $\frac { 7 } { 3 p ^ { 27 } }$ 
B)  $\frac { 7 p ^ { 27 } } { 3 }$ 
C)  $\frac { 7 } { 3 p ^ { 12 } }$ 
D)  $\frac { 7 p ^ { 12 } } { 3 }$ 
A)  $\frac { 7 } { 3 p ^ { 27 } }$ 
B)  $\frac { 7 p ^ { 27 } } { 3 }$ 
C)  $\frac { 7 } { 3 p ^ { 12 } }$ 
D)  $\frac { 7 p ^ { 12 } } { 3 }$

Question 5

Multiply using the FOIL method.
-$( b - 10 ) ( b + 2 )$

Accepted Answer

A)  $2 b ^ { 2 } + 20$ 
B)  $2 b - 20$ 
C)  $b ^ { 2 } + 8 b + 20$ 
D)  $b ^ { 2 } - 8 b - 20$ 
A)  $2 b ^ { 2 } + 20$ 
B)  $2 b - 20$ 
C)  $b ^ { 2 } + 8 b + 20$ 
D)  $b ^ { 2 } - 8 b - 20$

Question 6

Solve.
-The area of the playing surface of the tennis court shown is $\left( 9 x ^ { 2 } + 12 x - 32 \right)$ square feet. If its width is $( 3 x - 4 )$ feet, find its length.

Accepted Answer

A)  $( 15 x + 8 ) f t$ 
B)  $( 3 x + 8 ) \mathrm { ft }$ 
C)  $\left( 9 x ^ { 2 } + 93 x + 32 \right) f t$ 
D)  $( 3 x - 8 ) f t$ 
A)  $( 15 x + 8 ) f t$ 
B)  $( 3 x + 8 ) \mathrm { ft }$ 
C)  $\left( 9 x ^ { 2 } + 93 x + 32 \right) f t$ 
D)  $( 3 x - 8 ) f t$

Question 7

Multiply.
-$( a - 10 ) ( a + 10 )$

Accepted Answer

A)  $a ^ { 2 } + 20 a - 100$ 
B)  $a ^ { 2 } - 20$ 
C)  $a ^ { 2 } - 100$ 
D)  $a ^ { 2 } - 20 a - 100$ 
A)  $a ^ { 2 } + 20 a - 100$ 
B)  $a ^ { 2 } - 20$ 
C)  $a ^ { 2 } - 100$ 
D)  $a ^ { 2 } - 20 a - 100$

Question 8

Multiply.
-$\left( 4 x + \frac { 4 } { 9 } \right) \left( 4 x - \frac { 4 } { 9 } \right)$

Accepted Answer

A)  $16 x ^ { 2 } - \frac { 8 } { 9 }$ 
B)  $16 x ^ { 2 } - \frac { 32 } { 9 } x - \frac { 16 } { 81 }$ 
C)  $16 x ^ { 2 } + \frac { 32 } { 9 } x - \frac { 16 } { 81 }$ 
D)  $16 x ^ { 2 } - \frac { 16 } { 81 }$ 
A)  $16 x ^ { 2 } - \frac { 8 } { 9 }$ 
B)  $16 x ^ { 2 } - \frac { 32 } { 9 } x - \frac { 16 } { 81 }$ 
C)  $16 x ^ { 2 } + \frac { 32 } { 9 } x - \frac { 16 } { 81 }$ 
D)  $16 x ^ { 2 } - \frac { 16 } { 81 }$

Question 9

Simplify the expression. Write the result using positive exponents only.
-$\frac { - 7 y m ^ { 4 } n } { - 2 y m ^ { 7 } n }$

Accepted Answer

A)  $\frac { 1 } { 5 m ^ { 3 } }$ 
B)  $\frac { 5 } { m ^ { 3 } }$ 
C)  $\frac { 7 } { 2 m ^ { 3 } }$ 
D)  $\frac { 5 y ^ { 2 } n ^ { 2 } } { m ^ { 3 } }$ 
A)  $\frac { 1 } { 5 m ^ { 3 } }$ 
B)  $\frac { 5 } { m ^ { 3 } }$ 
C)  $\frac { 7 } { 2 m ^ { 3 } }$ 
D)  $\frac { 5 y ^ { 2 } n ^ { 2 } } { m ^ { 3 } }$

Question 10

Multiply.
-$- y \left( 6 x ^ { 3 } - 3 y + 3 x - 8 y ^ { 3 } \right)$

Accepted Answer

A)  $6 x ^ { 3 } y - 3 y ^ { 2 } + 3 x y ^ { 3 } - 8 y ^ { 4 }$ 
B)  $- 6 x ^ { 3 } + 3 x y ^ { 2 } - 3 x y ^ { 3 } + 8$ 
C)  $- 6 x ^ { 3 } + 3 x ^ { 2 } y - 3 y ^ { 2 } + 8 y ^ { 3 }$ 
D)  $- 6 x ^ { 3 } y + 3 y ^ { 2 } - 3 x y + 8 y ^ { 4 }$ 
A)  $6 x ^ { 3 } y - 3 y ^ { 2 } + 3 x y ^ { 3 } - 8 y ^ { 4 }$ 
B)  $- 6 x ^ { 3 } + 3 x y ^ { 2 } - 3 x y ^ { 3 } + 8$ 
C)  $- 6 x ^ { 3 } + 3 x ^ { 2 } y - 3 y ^ { 2 } + 8 y ^ { 3 }$ 
D)  $- 6 x ^ { 3 } y + 3 y ^ { 2 } - 3 x y + 8 y ^ { 4 }$

Question 11

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$P ( x ) = x ^ { 4 } + 3 x ^ { 3 } - 25 x ^ { 2 } + 15 x - 459 ; 5$

Accepted Answer

A)  $- 309$ 
B)  $- 9$ 
C)  $- 459$ 
D)  $- \frac { 9 } { 5 }$ 
A)  $- 309$ 
B)  $- 9$ 
C)  $- 459$ 
D)  $- \frac { 9 } { 5 }$

Question 12

Simplify.
-If $P ( x ) = 6 x + 8$, find $P ( - x )$.

Accepted Answer

A)  $6 x - 8$ 
B)  $- 14 x$ 
C)  $- 6 x - 8$ 
D)  $- 6 x + 8$ 
A)  $6 x - 8$ 
B)  $- 14 x$ 
C)  $- 6 x - 8$ 
D)  $- 6 x + 8$

Question 13

Write the number in standard notation.
-$4.756 \times 10 ^ { 6 }$

Accepted Answer

A)  $285.36$ 
B)  475,600 
C)  $4,756,000$ 
D)  $47,560,000$ 
A)  $285.36$ 
B)  475,600 
C)  $4,756,000$ 
D)  $47,560,000$

Question 14

Evaluate the expression using exponential rules. Write the result in standard notation.
-$\frac { 6 \times 10 ^ { - 2 } } { 30 \times 10 ^ { 3 } }$

Accepted Answer

A)  $0.000002$ 
B)  $- 0.000002$ 
C)  20,000 
D)  $- 20,000$ 
A)  $0.000002$ 
B)  $- 0.000002$ 
C)  20,000 
D)  $- 20,000$

Question 15

Find the quotient using long division.
-$\frac { x ^ { 3 } - 27 } { x - 3 }$

Accepted Answer

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

Question 16

Evaluate the expression using exponential rules. Write the result in standard notation.
-$\frac { 5.4 \times 10 ^ { 2 } } { 0.9 \times 10 ^ { - 4 } }$

Accepted Answer

A)  $6,000,000$ 
B)  $0.06$ 
C)  600,000 
D)  $0.006$ 
A)  $6,000,000$ 
B)  $0.06$ 
C)  600,000 
D)  $0.006$

Question 17

Perform the indicated operation.
-$\left( 9 x ^ { 3 } + 9 x ^ { 2 } + 4 x + 6 \right) + \left( 4 x ^ { 3 } + 2 x + 8 \right)$

Accepted Answer

A)  $13 x ^ { 3 } + 9 x ^ { 2 } + 6 x + 14$ 
B)  $13 x ^ { 3 } + 11 x ^ { 2 } + 8 x + 6$ 
C)  $4 x ^ { 3 } + 11 x ^ { 2 } + 12 x + 6$ 
D)  $13 x ^ { 3 } + 6 x + 14$ 
A)  $13 x ^ { 3 } + 9 x ^ { 2 } + 6 x + 14$ 
B)  $13 x ^ { 3 } + 11 x ^ { 2 } + 8 x + 6$ 
C)  $4 x ^ { 3 } + 11 x ^ { 2 } + 12 x + 6$ 
D)  $13 x ^ { 3 } + 6 x + 14$

Question 18

Perform the indicated operation.
-$\left( 5 x ^ { 8 } + 3 x ^ { 7 } - 6 x ^ { 2 } + 2 \right) - \left( 13 x ^ { 8 } - 7 x ^ { 4 } + 2 x ^ { 2 } - 13 \right)$

Accepted Answer

A)  $- 8 x ^ { 8 } + 3 x ^ { 7 } + 7 x ^ { 4 } - 8 x ^ { 2 } + 15$ 
B)  $8 x ^ { 8 } + 3 x ^ { 7 } - 7 x ^ { 4 } - 8 x ^ { 2 } + 15$ 
C)  $8 x ^ { 8 } + 3 x ^ { 7 } + 7 x ^ { 4 } - 8 x ^ { 2 } + 15$ 
D)  $- 8 x ^ { 8 } + 3 x ^ { 7 } - 7 x ^ { 4 } - 8 x ^ { 2 } + 15$ 
A)  $- 8 x ^ { 8 } + 3 x ^ { 7 } + 7 x ^ { 4 } - 8 x ^ { 2 } + 15$ 
B)  $8 x ^ { 8 } + 3 x ^ { 7 } - 7 x ^ { 4 } - 8 x ^ { 2 } + 15$ 
C)  $8 x ^ { 8 } + 3 x ^ { 7 } + 7 x ^ { 4 } - 8 x ^ { 2 } + 15$ 
D)  $- 8 x ^ { 8 } + 3 x ^ { 7 } - 7 x ^ { 4 } - 8 x ^ { 2 } + 15$

Question 19

Simplify the expression.
-$z ^ { 0 } + 7 ^ { 0 }$

Accepted Answer

A)  0 
B)  8 
C)  2 
D)  $z + 7$ 
A)  0 
B)  8 
C)  2 
D)  $z + 7$

Question 20

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

Accepted Answer

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

Multiply. - $( 2 a - 1 ) ^ { 2 }$

Multiply. - $( 10 z + 7 ) ^ { 2 }$

Multiply. - $( 8 x - 1 ) \left( x ^ { 2 } - 5 x + 1 \right)$

Simplify the expression. Write the result using positive exponents only. - $\frac { 7 p ^ { - 3 } } { 3 p ^ { 9 } }$

Multiply using the FOIL method. - $( b - 10 ) ( b + 2 )$

Multiply. - $( a - 10 ) ( a + 10 )$

Multiply. - $\left( 4 x + \frac { 4 } { 9 } \right) \left( 4 x - \frac { 4 } { 9 } \right)$

Simplify the expression. Write the result using positive exponents only. - $\frac { - 7 y m ^ { 4 } n } { - 2 y m ^ { 7 } n }$

Multiply. - $- y \left( 6 x ^ { 3 } - 3 y + 3 x - 8 y ^ { 3 } \right)$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = x ^ { 4 } + 3 x ^ { 3 } - 25 x ^ { 2 } + 15 x - 459 ; 5$

Simplify. -If $P ( x ) = 6 x + 8$ , find $P ( - x )$ .

Write the number in standard notation. - $4.756 \times 10 ^ { 6 }$

Evaluate the expression using exponential rules. Write the result in standard notation. - $\frac { 6 \times 10 ^ { - 2 } } { 30 \times 10 ^ { 3 } }$

Find the quotient using long division. - $\frac { x ^ { 3 } - 27 } { x - 3 }$

Evaluate the expression using exponential rules. Write the result in standard notation. - $\frac { 5.4 \times 10 ^ { 2 } } { 0.9 \times 10 ^ { - 4 } }$

Perform the indicated operation. - $\left( 9 x ^ { 3 } + 9 x ^ { 2 } + 4 x + 6 \right) + \left( 4 x ^ { 3 } + 2 x + 8 \right)$

Perform the indicated operation. - $\left( 5 x ^ { 8 } + 3 x ^ { 7 } - 6 x ^ { 2 } + 2 \right) - \left( 13 x ^ { 8 } - 7 x ^ { 4 } + 2 x ^ { 2 } - 13 \right)$

Simplify the expression. - $z ^ { 0 } + 7 ^ { 0 }$

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

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

Multiply. - (2a−1)2( 2 a - 1 ) ^ { 2 }(2a−1)2

Multiply. - (10z+7)2( 10 z + 7 ) ^ { 2 }(10z+7)2

Multiply. - (8x−1)(x2−5x+1)( 8 x - 1 ) \left( x ^ { 2 } - 5 x + 1 \right)(8x−1)(x2−5x+1)

Simplify the expression. Write the result using positive exponents only. - 7p−33p9\frac { 7 p ^ { - 3 } } { 3 p ^ { 9 } }3p97p−3​

Multiply using the FOIL method. - (b−10)(b+2)( b - 10 ) ( b + 2 )(b−10)(b+2)

Solve. -The area of the playing surface of the tennis court shown is (9x2+12x−32)\left( 9 x ^ { 2 } + 12 x - 32 \right)(9x2+12x−32) square feet. If its width is (3x−4)( 3 x - 4 )(3x−4) feet, find its length.

Multiply. - (a−10)(a+10)( a - 10 ) ( a + 10 )(a−10)(a+10)

Multiply. - (4x+49)(4x−49)\left( 4 x + \frac { 4 } { 9 } \right) \left( 4 x - \frac { 4 } { 9 } \right)(4x+94​)(4x−94​)

Simplify the expression. Write the result using positive exponents only. - −7ym4n−2ym7n\frac { - 7 y m ^ { 4 } n } { - 2 y m ^ { 7 } n }−2ym7n−7ym4n​

Multiply. - −y(6x3−3y+3x−8y3)- y \left( 6 x ^ { 3 } - 3 y + 3 x - 8 y ^ { 3 } \right)−y(6x3−3y+3x−8y3)

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - P(x)=x4+3x3−25x2+15x−459;5P ( x ) = x ^ { 4 } + 3 x ^ { 3 } - 25 x ^ { 2 } + 15 x - 459 ; 5P(x)=x4+3x3−25x2+15x−459;5

Simplify. -If P(x)=6x+8P ( x ) = 6 x + 8P(x)=6x+8 , find P(−x)P ( - x )P(−x) .

Write the number in standard notation. - 4.756×1064.756 \times 10 ^ { 6 }4.756×106

Evaluate the expression using exponential rules. Write the result in standard notation. - 6×10−230×103\frac { 6 \times 10 ^ { - 2 } } { 30 \times 10 ^ { 3 } }30×1036×10−2​

Find the quotient using long division. - x3−27x−3\frac { x ^ { 3 } - 27 } { x - 3 }x−3x3−27​

Evaluate the expression using exponential rules. Write the result in standard notation. - 5.4×1020.9×10−4\frac { 5.4 \times 10 ^ { 2 } } { 0.9 \times 10 ^ { - 4 } }0.9×10−45.4×102​

Perform the indicated operation. - (9x3+9x2+4x+6)+(4x3+2x+8)\left( 9 x ^ { 3 } + 9 x ^ { 2 } + 4 x + 6 \right) + \left( 4 x ^ { 3 } + 2 x + 8 \right)(9x3+9x2+4x+6)+(4x3+2x+8)

Perform the indicated operation. - (5x8+3x7−6x2+2)−(13x8−7x4+2x2−13)\left( 5 x ^ { 8 } + 3 x ^ { 7 } - 6 x ^ { 2 } + 2 \right) - \left( 13 x ^ { 8 } - 7 x ^ { 4 } + 2 x ^ { 2 } - 13 \right)(5x8+3x7−6x2+2)−(13x8−7x4+2x2−13)

Simplify the expression. - z0+70z ^ { 0 } + 7 ^ { 0 }z0+70

Multiply. - (12y+x)(12y−x)( 12 y + x ) ( 12 y - x )(12y+x)(12y−x)