Question 1

Find the product. $( 3 x + 6 ) ( 6 x - 3 )$

Accepted Answer

$18 x ^ { 2 } + 27 x - 18$

Question 2

Rearrange the polynomial in decreasing order; state the degree of the polynomial. $8 x + 8 x ^ { 2 } - 1$

Accepted Answer

A)  1st 
B)  8x 2 + 8x - 1 
C)  3rd 
D)  2nd 
E)  -1 + 8x 2 + 8x
F) 8x 2 + 8x + 8 
A)  1st 
B)  8x 2 + 8x - 1 
C)  3rd 
D)  2nd 
E)  -1 + 8x 2 + 8x
F) 8x 2 + 8x + 8 B,D

Question 3

Use the rule for exponents to simplify the following expression. $\left( - z ^ { 4 } x ^ { 6 } \right) ^ { 6 }$

Accepted Answer

$z ^ { 24 } x ^ { 36 }$

Question 4

Use the rule for exponents to simplify the following expression. $\left( - q ^ { 5 } x ^ { 5 } \right) ^ { 4 }$

Accepted Answer

A)  $q ^ { 20 } x ^ { 20 }$ 
B)  $( q x ) ^ { 100 }$ 
C)  $q ^ { 625 } x ^ { 625 }$ 
D)  $q ^ { 9 } x ^ { 9 }$ 
E)  $q ^ { 5 } x ^ { 20 }$ 
A)  $q ^ { 20 } x ^ { 20 }$ 
B)  $( q x ) ^ { 100 }$ 
C)  $q ^ { 625 } x ^ { 625 }$ 
D)  $q ^ { 9 } x ^ { 9 }$ 
E)  $q ^ { 5 } x ^ { 20 }$

Question 5

Find the product. $7 x ^ { 2 } y \left( 5 x ^ { 2 } - 7 x y + 9 y ^ { 2 } \right)$

Accepted Answer

The answer of Find the product. \(7 x ^ {...

Question 6

Divide. $\frac { - 18 a ^ { 6 } b ^ { 4 } } { - 16 a ^ { 2 } b ^ { 9 } }$

Accepted Answer

The answer of Divide. \(\frac { - 18 a ^...

Question 7

Evaluate the expression. $5 ( - 5 ) \div ( - 25 ) - ( - 8 ) \div 4$

Accepted Answer

The answer of Evaluate the expression. \(5 ( - 5...

Question 8

Simplify by first removing the parentheses and then combining the like terms. $( x + 5 ) - 10 ( 7 x - 2 )$

Accepted Answer

The answer of Simplify by first removing the parentheses and...

Question 9

Divide. $\frac { 45 w ^ { 4 } r ^ { 4 } + 54 w ^ { 3 } r ^ { 3 } - 63 w ^ { 2 } r ^ { 2 } } { 9 w ^ { 3 } r ^ { 3 } }$

Accepted Answer

The answer of Divide. \(\frac { 45 w ^ {...

Question 10

Divide. $\frac { b z ^ { 4 } - b z ^ { 3 } + b z ^ { 2 } - 7 b z } { - b z }$

Accepted Answer

A)  $- z ^ { 3 } + z ^ { 2 } - z + 7$ 
B)  $- b z ^ { 3 } + b z ^ { 2 } + b z + b + 7$ 
C)  $- z ^ { 3 } + z ^ { 2 } + z + 7$ 
D)  $- z ^ { 3 } + z ^ { 2 } - z + 7$ 
E)  $- b z ^ { 3 } + b z ^ { 2 } - b z + 7$ 
A)  $- z ^ { 3 } + z ^ { 2 } - z + 7$ 
B)  $- b z ^ { 3 } + b z ^ { 2 } + b z + b + 7$ 
C)  $- z ^ { 3 } + z ^ { 2 } + z + 7$ 
D)  $- z ^ { 3 } + z ^ { 2 } - z + 7$ 
E)  $- b z ^ { 3 } + b z ^ { 2 } - b z + 7$

Question 11

Find the product. $( 3 x + 2 ) ( 6 x - 7 )$

Accepted Answer

A)  $18 x ^ { 2 } - 33 x - 14$ 
B)  $18 x ^ { 2 } - 9 x - 14$ 
C)  $18 x ^ { 2 } - 11 x - 12$ 
D)  $18 x ^ { 2 } - 8 x - 15$ 
E)  $18 x ^ { 2 } - 6 x - 11$ 
A)  $18 x ^ { 2 } - 33 x - 14$ 
B)  $18 x ^ { 2 } - 9 x - 14$ 
C)  $18 x ^ { 2 } - 11 x - 12$ 
D)  $18 x ^ { 2 } - 8 x - 15$ 
E)  $18 x ^ { 2 } - 6 x - 11$

Question 12

Divide. $\left( z ^ { 7 } + z ^ { 6 } + z ^ { 5 } \right) \div z ^ { 5 }$

Accepted Answer

A)  $z ^ { 2 } + z + 1$ 
B)  $z ^ { 2 }$ 
C)  $z ^ { 2 } + z$ 
D)  $z + 1$ 
E)  $z ^ { 14 } + z ^ { 13 } + z ^ { 12 }$ 
A)  $z ^ { 2 } + z + 1$ 
B)  $z ^ { 2 }$ 
C)  $z ^ { 2 } + z$ 
D)  $z + 1$ 
E)  $z ^ { 14 } + z ^ { 13 } + z ^ { 12 }$

Question 13

Find the quotient and check. $\left( 54 m ^ { 2 } + 54 m + 12 \right) \div ( 9 m + 6 )$

Accepted Answer

A)  $12 m - 8$ 
B)  $6 m + 2$ 
C)  $6 m - 2$ 
D)  $11 m + 7$ 
E)  $9 m + 3$ 
A)  $12 m - 8$ 
B)  $6 m + 2$ 
C)  $6 m - 2$ 
D)  $11 m + 7$ 
E)  $9 m + 3$

Question 14

Use the rule for exponents to simplify the following expression. $\left( - 3 y ^ { 3 } z ^ { 2 } m ^ { 2 } \right) ^ { 4 }$

Accepted Answer

A)  $81 y ^ { 7 } z ^ { 6 } m ^ { 6 }$ 
B)  $81 y ^ { 13 } z ^ { 8 } m ^ { 9 }$ 
C)  $162 y ^ { 13 } z ^ { 9 } m ^ { 8 }$ 
D)  $- 162 y ^ { 12 } z ^ { 9 } m ^ { 8 }$ 
E)  $81 y ^ { 12 } z ^ { 8 } m ^ { 8 }$ 
A)  $81 y ^ { 7 } z ^ { 6 } m ^ { 6 }$ 
B)  $81 y ^ { 13 } z ^ { 8 } m ^ { 9 }$ 
C)  $162 y ^ { 13 } z ^ { 9 } m ^ { 8 }$ 
D)  $- 162 y ^ { 12 } z ^ { 9 } m ^ { 8 }$ 
E)  $81 y ^ { 12 } z ^ { 8 } m ^ { 8 }$

Question 15

Simplify by first removing the parentheses and then combining the like terms.   $6 - ( y + 9 ) + ( 5 y - 6 )$

Accepted Answer

A)  $9 y - 4$ 
B)  $- 9 y - 9$ 
C)  $- y - 21$ 
D)  $4 y - 9$ 
E)  $4 y + 3$ 
A)  $9 y - 4$ 
B)  $- 9 y - 9$ 
C)  $- y - 21$ 
D)  $4 y - 9$ 
E)  $4 y + 3$

Question 16

Use the rule for exponents to simplify. $\left( 6 z ^ { 5 } \right) ^ { 2 }$

Accepted Answer

The answer of Use the rule for exponents to simplify....

Question 17

Evaluate the expression when m=6. $\left( 2 m ^ { 2 } \right) ( - 6 m )$

Accepted Answer

The answer of Evaluate the expression when m=6. \(\left( 2...

Question 18

Find the product. $1.26 m \left( 2.8 m ^ { 2 } + 4.3 n ^ { 2 } \right)$

Accepted Answer

A)  $3.528 m ^ { 3 } + 3.651 m n ^ { 2 }$ 
B)  $3.528 m ^ { 3 } + 5.418 m n ^ { 2 }$ 
C)  $3.651 m ^ { 3 } + 5.295 m n ^ { 2 }$ 
D)  $3.873 m ^ { 3 } + 5.073 m n ^ { 2 }$ 
E)  $2.986 m ^ { 3 } + 5.96 m n ^ { 2 }$ 
A)  $3.528 m ^ { 3 } + 3.651 m n ^ { 2 }$ 
B)  $3.528 m ^ { 3 } + 5.418 m n ^ { 2 }$ 
C)  $3.651 m ^ { 3 } + 5.295 m n ^ { 2 }$ 
D)  $3.873 m ^ { 3 } + 5.073 m n ^ { 2 }$ 
E)  $2.986 m ^ { 3 } + 5.96 m n ^ { 2 }$

Question 19

Evaluate the expression. $9 \div ( - 3 ) ( 3 ) ^ { 3 } + 2 ( - 2 - 3 ) ^ { 2 } - ( - 4 ) ^ { 2 }$

Accepted Answer

The answer of Evaluate the expression. \(9 \div ( -...

Question 20

Let $X$ = $5$ and $y$ = $2$ and evaluate the expression. $\frac { 1 } { x } - \frac { 1 } { y } + \frac { 15 } { x y }$ Give your answer as a mixed number.

Accepted Answer

The answer of Let $X$ = $5$ and $y$ =...

Find the product. $( 3 x + 6 ) ( 6 x - 3 )$

Rearrange the polynomial in decreasing order; state the degree of the polynomial. $8 x + 8 x ^ { 2 } - 1$

Use the rule for exponents to simplify the following expression. $\left( - z ^ { 4 } x ^ { 6 } \right) ^ { 6 }$

Use the rule for exponents to simplify the following expression. $\left( - q ^ { 5 } x ^ { 5 } \right) ^ { 4 }$

Find the product. $7 x ^ { 2 } y \left( 5 x ^ { 2 } - 7 x y + 9 y ^ { 2 } \right)$

Divide. $\frac { - 18 a ^ { 6 } b ^ { 4 } } { - 16 a ^ { 2 } b ^ { 9 } }$

Evaluate the expression. $5 ( - 5 ) \div ( - 25 ) - ( - 8 ) \div 4$

Simplify by first removing the parentheses and then combining the like terms. $( x + 5 ) - 10 ( 7 x - 2 )$

Divide. $\frac { 45 w ^ { 4 } r ^ { 4 } + 54 w ^ { 3 } r ^ { 3 } - 63 w ^ { 2 } r ^ { 2 } } { 9 w ^ { 3 } r ^ { 3 } }$

Divide. $\frac { b z ^ { 4 } - b z ^ { 3 } + b z ^ { 2 } - 7 b z } { - b z }$

Find the product. $( 3 x + 2 ) ( 6 x - 7 )$

Divide. $\left( z ^ { 7 } + z ^ { 6 } + z ^ { 5 } \right) \div z ^ { 5 }$

Find the quotient and check. $\left( 54 m ^ { 2 } + 54 m + 12 \right) \div ( 9 m + 6 )$

Use the rule for exponents to simplify the following expression. $\left( - 3 y ^ { 3 } z ^ { 2 } m ^ { 2 } \right) ^ { 4 }$

Simplify by first removing the parentheses and then combining the like terms. $6 - ( y + 9 ) + ( 5 y - 6 )$

Use the rule for exponents to simplify. $\left( 6 z ^ { 5 } \right) ^ { 2 }$

Evaluate the expression when m=6. $\left( 2 m ^ { 2 } \right) ( - 6 m )$

Find the product. $1.26 m \left( 2.8 m ^ { 2 } + 4.3 n ^ { 2 } \right)$

Evaluate the expression. $9 \div ( - 3 ) ( 3 ) ^ { 3 } + 2 ( - 2 - 3 ) ^ { 2 } - ( - 4 ) ^ { 2 }$

Let $X$ = $5$ and $y$ = $2$ and evaluate the expression. $\frac { 1 } { x } - \frac { 1 } { y } + \frac { 15 } { x y }$ Give your answer as a mixed number.

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Equations and Formulas

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Quadratic Equations

Geometry

Right Triangle Trigonometry

Trigonometry With Any Angle

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Exam 5: Polynomials: an Introduction to Algebra

Find the product. (3x+6)(6x−3)( 3 x + 6 ) ( 6 x - 3 )(3x+6)(6x−3)

Rearrange the polynomial in decreasing order; state the degree of the polynomial. 8x+8x2−18 x + 8 x ^ { 2 } - 18x+8x2−1

Use the rule for exponents to simplify the following expression. (−z4x6)6\left( - z ^ { 4 } x ^ { 6 } \right) ^ { 6 }(−z4x6)6

Use the rule for exponents to simplify the following expression. (−q5x5)4\left( - q ^ { 5 } x ^ { 5 } \right) ^ { 4 }(−q5x5)4

Find the product. 7x2y(5x2−7xy+9y2)7 x ^ { 2 } y \left( 5 x ^ { 2 } - 7 x y + 9 y ^ { 2 } \right)7x2y(5x2−7xy+9y2)

Divide. −18a6b4−16a2b9\frac { - 18 a ^ { 6 } b ^ { 4 } } { - 16 a ^ { 2 } b ^ { 9 } }−16a2b9−18a6b4​

Evaluate the expression. 5(−5)÷(−25)−(−8)÷45 ( - 5 ) \div ( - 25 ) - ( - 8 ) \div 45(−5)÷(−25)−(−8)÷4

Simplify by first removing the parentheses and then combining the like terms. (x+5)−10(7x−2)( x + 5 ) - 10 ( 7 x - 2 )(x+5)−10(7x−2)

Divide. 45w4r4+54w3r3−63w2r29w3r3\frac { 45 w ^ { 4 } r ^ { 4 } + 54 w ^ { 3 } r ^ { 3 } - 63 w ^ { 2 } r ^ { 2 } } { 9 w ^ { 3 } r ^ { 3 } }9w3r345w4r4+54w3r3−63w2r2​

Divide. bz4−bz3+bz2−7bz−bz\frac { b z ^ { 4 } - b z ^ { 3 } + b z ^ { 2 } - 7 b z } { - b z }−bzbz4−bz3+bz2−7bz​

Find the product. (3x+2)(6x−7)( 3 x + 2 ) ( 6 x - 7 )(3x+2)(6x−7)

Divide. (z7+z6+z5)÷z5\left( z ^ { 7 } + z ^ { 6 } + z ^ { 5 } \right) \div z ^ { 5 }(z7+z6+z5)÷z5

Find the quotient and check. (54m2+54m+12)÷(9m+6)\left( 54 m ^ { 2 } + 54 m + 12 \right) \div ( 9 m + 6 )(54m2+54m+12)÷(9m+6)

Use the rule for exponents to simplify the following expression. (−3y3z2m2)4\left( - 3 y ^ { 3 } z ^ { 2 } m ^ { 2 } \right) ^ { 4 }(−3y3z2m2)4

Simplify by first removing the parentheses and then combining the like terms. 6−(y+9)+(5y−6)6 - ( y + 9 ) + ( 5 y - 6 )6−(y+9)+(5y−6)

Use the rule for exponents to simplify. (6z5)2\left( 6 z ^ { 5 } \right) ^ { 2 }(6z5)2

Evaluate the expression when m=6. (2m2)(−6m)\left( 2 m ^ { 2 } \right) ( - 6 m )(2m2)(−6m)

Find the product. 1.26m(2.8m2+4.3n2)1.26 m \left( 2.8 m ^ { 2 } + 4.3 n ^ { 2 } \right)1.26m(2.8m2+4.3n2)

Evaluate the expression. 9÷(−3)(3)3+2(−2−3)2−(−4)29 \div ( - 3 ) ( 3 ) ^ { 3 } + 2 ( - 2 - 3 ) ^ { 2 } - ( - 4 ) ^ { 2 }9÷(−3)(3)3+2(−2−3)2−(−4)2

Let XXX = 555 and yyy = 222 and evaluate the expression. 1x−1y+15xy\frac { 1 } { x } - \frac { 1 } { y } + \frac { 15 } { x y }x1​−y1​+xy15​ Give your answer as a mixed number.

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Equations and Formulas

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Quadratic Equations

Geometry

Right Triangle Trigonometry

Trigonometry With Any Angle

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Find the product. $( 3 x + 6 ) ( 6 x - 3 )$

Rearrange the polynomial in decreasing order; state the degree of the polynomial. $8 x + 8 x ^ { 2 } - 1$

Use the rule for exponents to simplify the following expression. $\left( - z ^ { 4 } x ^ { 6 } \right) ^ { 6 }$

Use the rule for exponents to simplify the following expression. $\left( - q ^ { 5 } x ^ { 5 } \right) ^ { 4 }$

Find the product. $7 x ^ { 2 } y \left( 5 x ^ { 2 } - 7 x y + 9 y ^ { 2 } \right)$

Divide. $\frac { - 18 a ^ { 6 } b ^ { 4 } } { - 16 a ^ { 2 } b ^ { 9 } }$

Evaluate the expression. $5 ( - 5 ) \div ( - 25 ) - ( - 8 ) \div 4$

Simplify by first removing the parentheses and then combining the like terms. $( x + 5 ) - 10 ( 7 x - 2 )$

Divide. $\frac { 45 w ^ { 4 } r ^ { 4 } + 54 w ^ { 3 } r ^ { 3 } - 63 w ^ { 2 } r ^ { 2 } } { 9 w ^ { 3 } r ^ { 3 } }$

Divide. $\frac { b z ^ { 4 } - b z ^ { 3 } + b z ^ { 2 } - 7 b z } { - b z }$

Find the product. $( 3 x + 2 ) ( 6 x - 7 )$

Divide. $\left( z ^ { 7 } + z ^ { 6 } + z ^ { 5 } \right) \div z ^ { 5 }$

Find the quotient and check. $\left( 54 m ^ { 2 } + 54 m + 12 \right) \div ( 9 m + 6 )$

Use the rule for exponents to simplify the following expression. $\left( - 3 y ^ { 3 } z ^ { 2 } m ^ { 2 } \right) ^ { 4 }$

Simplify by first removing the parentheses and then combining the like terms. $6 - ( y + 9 ) + ( 5 y - 6 )$

Use the rule for exponents to simplify. $\left( 6 z ^ { 5 } \right) ^ { 2 }$

Evaluate the expression when m=6. $\left( 2 m ^ { 2 } \right) ( - 6 m )$

Find the product. $1.26 m \left( 2.8 m ^ { 2 } + 4.3 n ^ { 2 } \right)$

Evaluate the expression. $9 \div ( - 3 ) ( 3 ) ^ { 3 } + 2 ( - 2 - 3 ) ^ { 2 } - ( - 4 ) ^ { 2 }$

Let $X$ = $5$ and $y$ = $2$ and evaluate the expression. $\frac { 1 } { x } - \frac { 1 } { y } + \frac { 15 } { x y }$ Give your answer as a mixed number.