Question 1

Multiply the following. (3 x )(2 x )

Accepted Answer

A)  $8 x$ 
B)  $6 x$ 
C)  $6 x ^ { 2 }$ 
D)  $3 x ^ { 2 }$ 
A)  $8 x$ 
B)  $6 x$ 
C)  $6 x ^ { 2 }$ 
D)  $3 x ^ { 2 }$

Question 2

Perform the division. $\left( x ^ { 4 } - 16 \right) \div ( x - 2 )$

Accepted Answer

The answer of Perform the division. \(\left( x ^ {...

Question 3

Find $( x + 6 ) ^ { 3 }$ . Don t forget that $( x + 6 ) ^ { 3 }$ means ( x + 6)( x + 6)( x + 6).

Accepted Answer

A)  $x ^ { 3 } + 6 x ^ { 2 } + 36 x + 216$ 
B)  $x ^ { 3 } + 18 x ^ { 2 } + 36 x + 216$ 
C)  $x ^ { 3 } + 18 x ^ { 2 } + 108 x + 36$ 
D)  $x ^ { 3 } + 18 x ^ { 2 } + 108 x + 216$ 
E)  none of these 
A)  $x ^ { 3 } + 6 x ^ { 2 } + 36 x + 216$ 
B)  $x ^ { 3 } + 18 x ^ { 2 } + 36 x + 216$ 
C)  $x ^ { 3 } + 18 x ^ { 2 } + 108 x + 36$ 
D)  $x ^ { 3 } + 18 x ^ { 2 } + 108 x + 216$ 
E)  none of these

Question 4

Perform the division. $\left( x ^ { 2 } + 19 x + 60 \right) \div ( x + 4 )$

Accepted Answer

The answer of Perform the division. \(\left( x ^ {...

Question 5

Perform the division. $\left( x ^ { 4 } - 81 \right) \div ( x - 3 )$

Accepted Answer

A)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27$ 
B)  $x ^ { 3 } - 3 x ^ { 2 } + 9 x - 27$ 
C)  $x ^ { 2 } - 12 x - 27$ 
D)  $x ^ { 3 } - 12 x + 27$ 
A)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27$ 
B)  $x ^ { 3 } - 3 x ^ { 2 } + 9 x - 27$ 
C)  $x ^ { 2 } - 12 x - 27$ 
D)  $x ^ { 3 } - 12 x + 27$

Question 6

Multiply by using the distributive property. $- 3 y \left( 6 y ^ { 2 } - 6 y - 7 \right)$

Accepted Answer

A)  $- 18 y ^ { 3 } + 6 y ^ { 2 } + 21 y$ 
B)  $- 18 y ^ { 3 } + 18 y ^ { 2 } + 21 y$ 
C)  $- 18 y ^ { 3 } + 18 y ^ { 2 } + 7 y$ 
D)  $- 3 y ^ { 3 } + 18 y ^ { 2 } + 21 y$ 
E)  $- 18 y ^ { 3 } + 6 y ^ { 2 } + 7 y$ 
A)  $- 18 y ^ { 3 } + 6 y ^ { 2 } + 21 y$ 
B)  $- 18 y ^ { 3 } + 18 y ^ { 2 } + 21 y$ 
C)  $- 18 y ^ { 3 } + 18 y ^ { 2 } + 7 y$ 
D)  $- 3 y ^ { 3 } + 18 y ^ { 2 } + 21 y$ 
E)  $- 18 y ^ { 3 } + 6 y ^ { 2 } + 7 y$

Question 7

Divide the monomials. $\frac { - 20 y ^ { 6 } m ^ { 11 } a ^ { 7 } } { 5 y ^ { 3 } m ^ { 5 } a ^ { 3 } }$

Accepted Answer

A)  $- 4 y ^ { 2 } m ^ { 6 } a ^ { 2 }$ 
B)  $- 4 y ^ { 3 } m ^ { 8 } a ^ { 4 }$ 
C)  $- 4 y ^ { 3 } m ^ { 6 } a ^ { 4 }$ 
D)  $- 4 y ^ { 3 } m ^ { 6 } a ^ { 2 }$ 
E)  $- 4 y ^ { 3 } m ^ { 8 } a ^ { 6 }$ 
A)  $- 4 y ^ { 2 } m ^ { 6 } a ^ { 2 }$ 
B)  $- 4 y ^ { 3 } m ^ { 8 } a ^ { 4 }$ 
C)  $- 4 y ^ { 3 } m ^ { 6 } a ^ { 4 }$ 
D)  $- 4 y ^ { 3 } m ^ { 6 } a ^ { 2 }$ 
E)  $- 4 y ^ { 3 } m ^ { 8 } a ^ { 6 }$

Question 8

Find the product by using the shortcut pattern for multiplying binomials. $( 2 n - 3 ) ( 6 n - 5 )$

Accepted Answer

A)  $12 n ^ { 2 } - 28 n + 15$ 
B)  $12 n ^ { 2 } - 30 n + 15$ 
C)  $12 n ^ { 2 } - 26 n - 15$ 
D)  $12 n ^ { 2 } + 32 n + 8$ 
E)  $12 n ^ { 2 } + 34 n - 8$ 
A)  $12 n ^ { 2 } - 28 n + 15$ 
B)  $12 n ^ { 2 } - 30 n + 15$ 
C)  $12 n ^ { 2 } - 26 n - 15$ 
D)  $12 n ^ { 2 } + 32 n + 8$ 
E)  $12 n ^ { 2 } + 34 n - 8$

Question 9

Use scientific notation and the properties of exponents to evaluate the following numerical expression. $\frac { ( 0.00006 ) ( 2,000 ) } { ( 0.002 ) ( 40 ) }$

Accepted Answer

A)  $1.5$ 
B)  $0.25$ 
C)  $0.015$ 
D)  $2$ 
E)  $0.15$ 
A)  $1.5$ 
B)  $0.25$ 
C)  $0.015$ 
D)  $2$ 
E)  $0.15$

Question 10

Divide the monomials. $\frac { - 40 y ^ { 4 } q ^ { 10 } } { 5 q ^ { 2 } }$

Accepted Answer

A)  $- 8 y ^ { 3 } q ^ { 13 }$ 
B)  $- 8 q ^ { 8 }$ 
C)  $- 8 y ^ { 4 } q ^ { 10 }$ 
D)  $- 8 y ^ { 4 } q ^ { 8 }$ 
E)  $- 8 y ^ { 3 } q ^ { 9 }$ 
A)  $- 8 y ^ { 3 } q ^ { 13 }$ 
B)  $- 8 q ^ { 8 }$ 
C)  $- 8 y ^ { 4 } q ^ { 10 }$ 
D)  $- 8 y ^ { 4 } q ^ { 8 }$ 
E)  $- 8 y ^ { 3 } q ^ { 9 }$

Question 11

Subtract the sum of 10 x + 16 and 4 x + 10 from 7 x + 6.

Accepted Answer

A)  $-$ x $-$ 29 
B)  $-$ x $-$ 16 
C)  $-$ 7 x + 20 
D)  $-$ 7 x $-$ 20 
E)  7 x + 20 
A)  $-$ x $-$ 29 
B)  $-$ x $-$ 16 
C)  $-$ 7 x + 20 
D)  $-$ 7 x $-$ 20 
E)  7 x + 20

Question 12

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( 2 y ^ { 5 } \right) ^ { 3 }$ Enter your answer as $k y ^ { p }$ where k , p are numbers and y is a variable.

Accepted Answer

The answer of Raise the monomial to the indicated power....

Question 13

Perform the division. $\left( 5 n ^ { 2 } - 23 n - 10 \right) \div ( n - 5 )$

Accepted Answer

The answer of Perform the division. \(\left( 5 n ^...

Question 14

Perform the division and find the remainder. $\left( x ^ { 3 } - 3 x ^ { 2 } - 5 x + 3 \right) \div \left( x ^ { 2 } + 2 x \right)$

Accepted Answer

A)  5 - 3 x 
B)  3 x - 5 
C)  5 x - 3 
D)  3 x + 5 
E)  5 x + 3 
A)  5 - 3 x 
B)  3 x - 5 
C)  5 x - 3 
D)  3 x + 5 
E)  5 x + 3

Question 15

Evaluate the numerical expression. $4 ^ { - 3 }$

Accepted Answer

A)  $\frac { 1 } { 16 }$ 
B)  $- \frac { 1 } { 64 }$ 
C)  $\frac { 1 } { 64 }$ 
D)  $- \frac { 1 } { 16 }$ 
E)  $64$ 
A)  $\frac { 1 } { 16 }$ 
B)  $- \frac { 1 } { 64 }$ 
C)  $\frac { 1 } { 64 }$ 
D)  $- \frac { 1 } { 16 }$ 
E)  $64$

Question 16

Add the polynomials. $10 y ^ { 5 } + 7 y + 13 \text { and } - 4 y ^ { 5 } - 2 y + 14$

Accepted Answer

The answer of Add the polynomials. \(10 y ^ {...

Question 17

Subtract the polynomials using a vertical format. $- 6 z ^ { 5 } - 1 \text { from } - 5 z ^ { 5 } + 2$

Accepted Answer

The answer of Subtract the polynomials using a vertical format....

Question 18

Multiply by using the distributive property. $2 a ( 4 a + 5 )$

Accepted Answer

A)  $8 a + 10$ 
B)  $8 a ^ { 2 } + 5 a$ 
C)  $2 a ^ { 2 } + 10 a$ 
D)  $8 a ^ { 2 } + 10$ 
E)  $8 a ^ { 2 } + 10 a$ 
A)  $8 a + 10$ 
B)  $8 a ^ { 2 } + 5 a$ 
C)  $2 a ^ { 2 } + 10 a$ 
D)  $8 a ^ { 2 } + 10$ 
E)  $8 a ^ { 2 } + 10 a$

Question 19

Represent the area of the shaded region in the following figure. The length of a radius of the smaller circle is x , and the length of a radius of the larger circle is 5 x .

Accepted Answer

A)  $23 \pi x$ 
B)  $25 x ^ { 2 }$ 
C)  $24 \pi x$ 
D)  $24 \pi x ^ { 2 }$ 
E)  $25 \pi x ^ { 2 }$ 
A)  $23 \pi x$ 
B)  $25 x ^ { 2 }$ 
C)  $24 \pi x$ 
D)  $24 \pi x ^ { 2 }$ 
E)  $25 \pi x ^ { 2 }$

Question 20

Use one of the appropriate patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$ $( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$ $( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ to find the following product. $- 6 x ( 3 - 6 x ) ( 3 + 6 x )$

Accepted Answer

A)  $- 18 x + 216 x ^ { 3 }$ 
B)  $- 18 x + 36 x ^ { 3 }$ 
C)  $- 54 x + 216 x ^ { 3 }$ 
D)  $- 54 x + 36 x ^ { 3 }$ 
E)  $- 54 x - 216 x ^ { 2 }$ 
A)  $- 18 x + 216 x ^ { 3 }$ 
B)  $- 18 x + 36 x ^ { 3 }$ 
C)  $- 54 x + 216 x ^ { 3 }$ 
D)  $- 54 x + 36 x ^ { 3 }$ 
E)  $- 54 x - 216 x ^ { 2 }$

Multiply the following. (3 x )(2 x )

Perform the division. $\left( x ^ { 4 } - 16 \right) \div ( x - 2 )$

Find $( x + 6 ) ^ { 3 }$ . Don t forget that $( x + 6 ) ^ { 3 }$ means ( x + 6)( x + 6)( x + 6).

Perform the division. $\left( x ^ { 2 } + 19 x + 60 \right) \div ( x + 4 )$

Perform the division. $\left( x ^ { 4 } - 81 \right) \div ( x - 3 )$

Multiply by using the distributive property. $- 3 y \left( 6 y ^ { 2 } - 6 y - 7 \right)$

Divide the monomials. $\frac { - 20 y ^ { 6 } m ^ { 11 } a ^ { 7 } } { 5 y ^ { 3 } m ^ { 5 } a ^ { 3 } }$

Find the product by using the shortcut pattern for multiplying binomials. $( 2 n - 3 ) ( 6 n - 5 )$

Use scientific notation and the properties of exponents to evaluate the following numerical expression. $\frac { ( 0.00006 ) ( 2,000 ) } { ( 0.002 ) ( 40 ) }$

Divide the monomials. $\frac { - 40 y ^ { 4 } q ^ { 10 } } { 5 q ^ { 2 } }$

Subtract the sum of 10 x + 16 and 4 x + 10 from 7 x + 6.

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( 2 y ^ { 5 } \right) ^ { 3 }$ Enter your answer as $k y ^ { p }$ where k , p are numbers and y is a variable.

Perform the division. $\left( 5 n ^ { 2 } - 23 n - 10 \right) \div ( n - 5 )$

Perform the division and find the remainder. $\left( x ^ { 3 } - 3 x ^ { 2 } - 5 x + 3 \right) \div \left( x ^ { 2 } + 2 x \right)$

Evaluate the numerical expression. $4 ^ { - 3 }$

Add the polynomials. $10 y ^ { 5 } + 7 y + 13 \text { and } - 4 y ^ { 5 } - 2 y + 14$

Subtract the polynomials using a vertical format. $- 6 z ^ { 5 } - 1 \text { from } - 5 z ^ { 5 } + 2$

Multiply by using the distributive property. $2 a ( 4 a + 5 )$

Represent the area of the shaded region in the following figure. The length of a radius of the smaller circle is x , and the length of a radius of the larger circle is 5 x .

Use one of the appropriate patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$ $( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$ $( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ to find the following product. $- 6 x ( 3 - 6 x ) ( 3 + 6 x )$

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 6: Exponents and Polynomials

Multiply the following. (3 x )(2 x )

Perform the division. (x4−16)÷(x−2)\left( x ^ { 4 } - 16 \right) \div ( x - 2 )(x4−16)÷(x−2)

Find (x+6)3( x + 6 ) ^ { 3 }(x+6)3 . Don t forget that (x+6)3( x + 6 ) ^ { 3 }(x+6)3 means ( x + 6)( x + 6)( x + 6).

Perform the division. (x2+19x+60)÷(x+4)\left( x ^ { 2 } + 19 x + 60 \right) \div ( x + 4 )(x2+19x+60)÷(x+4)

Perform the division. (x4−81)÷(x−3)\left( x ^ { 4 } - 81 \right) \div ( x - 3 )(x4−81)÷(x−3)

Multiply by using the distributive property. −3y(6y2−6y−7)- 3 y \left( 6 y ^ { 2 } - 6 y - 7 \right)−3y(6y2−6y−7)

Divide the monomials. −20y6m11a75y3m5a3\frac { - 20 y ^ { 6 } m ^ { 11 } a ^ { 7 } } { 5 y ^ { 3 } m ^ { 5 } a ^ { 3 } }5y3m5a3−20y6m11a7​

Find the product by using the shortcut pattern for multiplying binomials. (2n−3)(6n−5)( 2 n - 3 ) ( 6 n - 5 )(2n−3)(6n−5)

Use scientific notation and the properties of exponents to evaluate the following numerical expression. (0.00006)(2,000)(0.002)(40)\frac { ( 0.00006 ) ( 2,000 ) } { ( 0.002 ) ( 40 ) }(0.002)(40)(0.00006)(2,000)​

Divide the monomials. −40y4q105q2\frac { - 40 y ^ { 4 } q ^ { 10 } } { 5 q ^ { 2 } }5q2−40y4q10​

Subtract the sum of 10 x + 16 and 4 x + 10 from 7 x + 6.

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. (2y5)3\left( 2 y ^ { 5 } \right) ^ { 3 }(2y5)3 Enter your answer as kypk y ^ { p }kyp where k , p are numbers and y is a variable.

Perform the division. (5n2−23n−10)÷(n−5)\left( 5 n ^ { 2 } - 23 n - 10 \right) \div ( n - 5 )(5n2−23n−10)÷(n−5)

Perform the division and find the remainder. (x3−3x2−5x+3)÷(x2+2x)\left( x ^ { 3 } - 3 x ^ { 2 } - 5 x + 3 \right) \div \left( x ^ { 2 } + 2 x \right)(x3−3x2−5x+3)÷(x2+2x)

Evaluate the numerical expression. 4−34 ^ { - 3 }4−3

Add the polynomials. 10y5+7y+13 and −4y5−2y+1410 y ^ { 5 } + 7 y + 13 \text { and } - 4 y ^ { 5 } - 2 y + 1410y5+7y+13 and −4y5−2y+14

Subtract the polynomials using a vertical format. −6z5−1 from −5z5+2- 6 z ^ { 5 } - 1 \text { from } - 5 z ^ { 5 } + 2−6z5−1 from −5z5+2

Multiply by using the distributive property. 2a(4a+5)2 a ( 4 a + 5 )2a(4a+5)

Represent the area of the shaded region in the following figure. The length of a radius of the smaller circle is x , and the length of a radius of the larger circle is 5 x .

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Perform the division. $\left( x ^ { 4 } - 16 \right) \div ( x - 2 )$

Find $( x + 6 ) ^ { 3 }$ . Don t forget that $( x + 6 ) ^ { 3 }$ means ( x + 6)( x + 6)( x + 6).

Perform the division. $\left( x ^ { 2 } + 19 x + 60 \right) \div ( x + 4 )$

Perform the division. $\left( x ^ { 4 } - 81 \right) \div ( x - 3 )$

Multiply by using the distributive property. $- 3 y \left( 6 y ^ { 2 } - 6 y - 7 \right)$

Divide the monomials. $\frac { - 20 y ^ { 6 } m ^ { 11 } a ^ { 7 } } { 5 y ^ { 3 } m ^ { 5 } a ^ { 3 } }$

Find the product by using the shortcut pattern for multiplying binomials. $( 2 n - 3 ) ( 6 n - 5 )$

Use scientific notation and the properties of exponents to evaluate the following numerical expression. $\frac { ( 0.00006 ) ( 2,000 ) } { ( 0.002 ) ( 40 ) }$

Divide the monomials. $\frac { - 40 y ^ { 4 } q ^ { 10 } } { 5 q ^ { 2 } }$

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( 2 y ^ { 5 } \right) ^ { 3 }$ Enter your answer as $k y ^ { p }$ where k , p are numbers and y is a variable.

Perform the division. $\left( 5 n ^ { 2 } - 23 n - 10 \right) \div ( n - 5 )$

Perform the division and find the remainder. $\left( x ^ { 3 } - 3 x ^ { 2 } - 5 x + 3 \right) \div \left( x ^ { 2 } + 2 x \right)$

Evaluate the numerical expression. $4 ^ { - 3 }$

Add the polynomials. $10 y ^ { 5 } + 7 y + 13 \text { and } - 4 y ^ { 5 } - 2 y + 14$

Subtract the polynomials using a vertical format. $- 6 z ^ { 5 } - 1 \text { from } - 5 z ^ { 5 } + 2$

Multiply by using the distributive property. $2 a ( 4 a + 5 )$