Question 1

Perform the division and find the remainder. $\left( 16 n ^ { 2 } + 32 n - 32 \right) \div ( 4 n + 10 )$

Accepted Answer

A)  $- 6$ 
B)  $14$ 
C)  $- 14$ 
D)  $- 12$ 
E)  $12$ 
A)  $- 6$ 
B)  $14$ 
C)  $- 14$ 
D)  $- 12$ 
E)  $12$

Question 2

Multiply. $( 8 c d ) \left( - 7 c ^ { 5 } d \right) ( - 4 d )$

Accepted Answer

A)  $224 c ^ { 5 } d$ 
B)  $- 223 c ^ { 6 } d ^ { 3 }$ 
C)  $221 c ^ { 6 } d ^ { 2 }$ 
D)  $- 224 c ^ { 5 } d ^ { 3 }$ 
E)  $224 c ^ { 6 } d ^ { 3 }$ 
A)  $224 c ^ { 5 } d$ 
B)  $- 223 c ^ { 6 } d ^ { 3 }$ 
C)  $221 c ^ { 6 } d ^ { 2 }$ 
D)  $- 224 c ^ { 5 } d ^ { 3 }$ 
E)  $224 c ^ { 6 } d ^ { 3 }$

Question 3

Simplify the following algebraic expression and express your answer using positive exponents only. $x ^ { 8 } x ^ { - 6 }$

Accepted Answer

The answer of Simplify the following algebraic expression and express...

Question 4

Add the polynomials. $5 p ^ { 2 } + 4 p + 15 \text { and } - 5 p ^ { 2 } - 9 p + 10$

Accepted Answer

The answer of Add the polynomials. \(5 p ^ {...

Question 5

Perform the division of the polynomials by monomials. $\frac { - 96 z ^ { 6 } c ^ { 7 } - 96 z ^ { 12 } c ^ { 10 } } { - 12 z ^ { 3 } c ^ { 4 } }$

Accepted Answer

A)  $8 z ^ { 3 } c ^ { 3 } + 8 z ^ { 9 } c ^ { 6 }$ 
B)  $8 z ^ { 4 } c ^ { 2 } + 8 z ^ { 9 } c ^ { 6 }$ 
C)  $8 z ^ { 3 } c ^ { 3 } + 8 z ^ { 10 } c ^ { 7 }$ 
D)  $8 z ^ { 3 } c ^ { 3 } - 8 z ^ { 10 } c ^ { 6 }$ 
A)  $8 z ^ { 3 } c ^ { 3 } + 8 z ^ { 9 } c ^ { 6 }$ 
B)  $8 z ^ { 4 } c ^ { 2 } + 8 z ^ { 9 } c ^ { 6 }$ 
C)  $8 z ^ { 3 } c ^ { 3 } + 8 z ^ { 10 } c ^ { 7 }$ 
D)  $8 z ^ { 3 } c ^ { 3 } - 8 z ^ { 10 } c ^ { 6 }$

Question 6

Find the indicated product by applying the distributive property and combining similar terms. $( x + 8 ) \left( x ^ { 2 } - 6 x - 3 \right)$

Accepted Answer

A)  $x ^ { 3 } + 2 x ^ { 2 } - 51 x - 24$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } - 51 x - 8$ 
C)  $x ^ { 3 } + 8 x ^ { 2 } - 51 x - 24$ 
D)  $x ^ { 3 } + 2 x ^ { 2 } - 48 x - 24$ 
E)  none of these 
A)  $x ^ { 3 } + 2 x ^ { 2 } - 51 x - 24$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } - 51 x - 8$ 
C)  $x ^ { 3 } + 8 x ^ { 2 } - 51 x - 24$ 
D)  $x ^ { 3 } + 2 x ^ { 2 } - 48 x - 24$ 
E)  none of these

Question 7

Perform the division of the polynomials by monomials. $\frac { - 44 z ^ { 6 } - 110 z ^ { 11 } } { - 11 z ^ { 3 } }$

Accepted Answer

A)  $- 4 z ^ { 3 } + 10 z ^ { 11 }$ 
B)  $4 z ^ { 3 } + 10 z ^ { 11 }$ 
C)  $4 z ^ { 4 } + 10 z ^ { 8 }$ 
D)  $4 z ^ { 3 } + 10 z ^ { 8 }$ 
A)  $- 4 z ^ { 3 } + 10 z ^ { 11 }$ 
B)  $4 z ^ { 3 } + 10 z ^ { 11 }$ 
C)  $4 z ^ { 4 } + 10 z ^ { 8 }$ 
D)  $4 z ^ { 3 } + 10 z ^ { 8 }$

Question 8

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 7 b ^ { - 6 } \right) \left( 2 b ^ { 9 } \right)$

Accepted Answer

The answer of Simplify the following algebraic expression and express...

Question 9

Simplify the following algebraic expression and express your answer using positive exponents only. $\frac { b ^ { - 4 } } { b ^ { 6 } }$

Accepted Answer

A)  $- \frac { 1 } { b ^ { 10 } }$ 
B)  $b ^ { 2 }$ 
C)  $\frac { 1 } { b ^ { 2 } }$ 
D)  $b ^ { 10 }$ 
E)  $\frac { 1 } { b ^ { 10 } }$ 
A)  $- \frac { 1 } { b ^ { 10 } }$ 
B)  $b ^ { 2 }$ 
C)  $\frac { 1 } { b ^ { 2 } }$ 
D)  $b ^ { 10 }$ 
E)  $\frac { 1 } { b ^ { 10 } }$

Question 10

Perform the division of the polynomials by monomials. $\frac { 48 p ^ { 8 } d ^ { 7 } + 56 p ^ { 15 } d ^ { 11 } } { 8 p ^ { 2 } d ^ { 2 } }$

Accepted Answer

The answer of Perform the division of the polynomials by...

Question 11

Find the indicated product by applying the distributive property and combining similar terms. (3 x $-$ 5) (3 x $-$ 9)

Accepted Answer

A)  $9 x ^ { 2 } - 42 x + 45$ 
B)  $9 x ^ { 2 } - 42 x$ 
C)  $9 x ^ { 2 } - 27 x + 45$ 
D)  $9 x ^ { 2 } + 42 x + 45$ 
E)  $9 x ^ { 2 } - 42 x - 45$ 
A)  $9 x ^ { 2 } - 42 x + 45$ 
B)  $9 x ^ { 2 } - 42 x$ 
C)  $9 x ^ { 2 } - 27 x + 45$ 
D)  $9 x ^ { 2 } + 42 x + 45$ 
E)  $9 x ^ { 2 } - 42 x - 45$

Question 12

Perform the indicated operations. $( 3 z + 3 ) - ( 8 z - 11 ) + ( 9 z + 3 )$

Accepted Answer

A)  $4 z + 17$ 
B)  $4 z - 17$ 
C)  $- 4 z - 17$ 
D)  $- 4 z + 17$ 
A)  $4 z + 17$ 
B)  $4 z - 17$ 
C)  $- 4 z - 17$ 
D)  $- 4 z + 17$

Question 13

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( 2 a ^ { 3 } \right) ^ { 2 }$

Accepted Answer

A)  $2 a ^ { 6 }$ 
B)  $4 a ^ { 5 }$ 
C)  $4 a ^ { 6 }$ 
D)  $2 a ^ { 5 }$ 
A)  $2 a ^ { 6 }$ 
B)  $4 a ^ { 5 }$ 
C)  $4 a ^ { 6 }$ 
D)  $2 a ^ { 5 }$

Question 14

When raising a power to a power, add exponents.

Accepted Answer

A) True 
 B)False

Question 15

Subtract the polynomials using a horizontal format. $4 p ^ { 4 } - 11 p + 2 \text { from } 2 p ^ { 4 } + 5 p + 10$

Accepted Answer

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

Question 16

Divide the polynomial by the monomial. $\frac { - 24 z ^ { 11 } - 72 z ^ { 15 } } { - 12 z ^ { 3 } }$

Accepted Answer

A)  $2 z ^ { 9 } + 6 z ^ { 12 }$ 
B)  $2 z ^ { 8 } + 6 z ^ { 12 }$ 
C)  $- 2 z ^ { 8 } + 6 z ^ { 15 }$ 
D)  $2 z ^ { 8 } + 6 z ^ { 15 }$ 
E)  $- 2 z ^ { 8 } + 6 z ^ { 12 }$ 
A)  $2 z ^ { 9 } + 6 z ^ { 12 }$ 
B)  $2 z ^ { 8 } + 6 z ^ { 12 }$ 
C)  $- 2 z ^ { 8 } + 6 z ^ { 15 }$ 
D)  $2 z ^ { 8 } + 6 z ^ { 15 }$ 
E)  $- 2 z ^ { 8 } + 6 z ^ { 12 }$

Question 17

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. $- 9 x ( 4 - 9 x ) ( 4 + 9 x )$

Accepted Answer

A)  $- 36 x + 729 x ^ { 3 }$ 
B)  $- 144 x + 729 x ^ { 3 }$ 
C)  $- 144 x - 729 x ^ { 2 }$ 
D)  $- 144 x + 81 x ^ { 3 }$ 
E)  none of these 
A)  $- 36 x + 729 x ^ { 3 }$ 
B)  $- 144 x + 729 x ^ { 3 }$ 
C)  $- 144 x - 729 x ^ { 2 }$ 
D)  $- 144 x + 81 x ^ { 3 }$ 
E)  none of these

Question 18

Write the following number in standard decimal form. $( 4.03 ) \left( 10 ^ { 5 } \right)$

Accepted Answer

A)  40,300,000 
B)  4,030 
C)  403,000 
D)  4,030,000 
A)  40,300,000 
B)  4,030 
C)  403,000 
D)  4,030,000

Question 19

Find the product by using the shortcut pattern for multiplying binomials. $( 2 a + 9 ) ( a + 2 )$

Accepted Answer

A)  $2 a ^ { 2 } + 13 a + 18$ 
B)  $2 a ^ { 2 } + 13 a + 34$ 
C)  $2 a ^ { 2 } + 17 a + 40$ 
D)  $2 a ^ { 2 } + 17 a + 18$ 
E)  $2 a ^ { 2 } + 13 a + 40$ 
A)  $2 a ^ { 2 } + 13 a + 18$ 
B)  $2 a ^ { 2 } + 13 a + 34$ 
C)  $2 a ^ { 2 } + 17 a + 40$ 
D)  $2 a ^ { 2 } + 17 a + 18$ 
E)  $2 a ^ { 2 } + 13 a + 40$

Question 20

Divide the monomials. $\frac { 2 y ^ { 5 } q ^ { 11 } } { y ^ { 3 } q ^ { 4 } }$

Accepted Answer

A)  $2 y ^ { 2 } q ^ { 8 }$ 
B)  $2 y ^ { 1 } q ^ { 11 }$ 
C)  $2 y ^ { 2 } q ^ { 7 }$ 
D)  $2 y ^ { 4 } q ^ { 7 }$ 
E)  $2 y ^ { 3 } q ^ { 8 }$ 
A)  $2 y ^ { 2 } q ^ { 8 }$ 
B)  $2 y ^ { 1 } q ^ { 11 }$ 
C)  $2 y ^ { 2 } q ^ { 7 }$ 
D)  $2 y ^ { 4 } q ^ { 7 }$ 
E)  $2 y ^ { 3 } q ^ { 8 }$

Perform the division and find the remainder. $\left( 16 n ^ { 2 } + 32 n - 32 \right) \div ( 4 n + 10 )$

Multiply. $( 8 c d ) \left( - 7 c ^ { 5 } d \right) ( - 4 d )$

Simplify the following algebraic expression and express your answer using positive exponents only. $x ^ { 8 } x ^ { - 6 }$

Add the polynomials. $5 p ^ { 2 } + 4 p + 15 \text { and } - 5 p ^ { 2 } - 9 p + 10$

Perform the division of the polynomials by monomials. $\frac { - 96 z ^ { 6 } c ^ { 7 } - 96 z ^ { 12 } c ^ { 10 } } { - 12 z ^ { 3 } c ^ { 4 } }$

Find the indicated product by applying the distributive property and combining similar terms. $( x + 8 ) \left( x ^ { 2 } - 6 x - 3 \right)$

Perform the division of the polynomials by monomials. $\frac { - 44 z ^ { 6 } - 110 z ^ { 11 } } { - 11 z ^ { 3 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 7 b ^ { - 6 } \right) \left( 2 b ^ { 9 } \right)$

Simplify the following algebraic expression and express your answer using positive exponents only. $\frac { b ^ { - 4 } } { b ^ { 6 } }$

Perform the division of the polynomials by monomials. $\frac { 48 p ^ { 8 } d ^ { 7 } + 56 p ^ { 15 } d ^ { 11 } } { 8 p ^ { 2 } d ^ { 2 } }$

Find the indicated product by applying the distributive property and combining similar terms. (3 x $-$ 5) (3 x $-$ 9)

Perform the indicated operations. $( 3 z + 3 ) - ( 8 z - 11 ) + ( 9 z + 3 )$

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( 2 a ^ { 3 } \right) ^ { 2 }$

When raising a power to a power, add exponents.

Subtract the polynomials using a horizontal format. $4 p ^ { 4 } - 11 p + 2 \text { from } 2 p ^ { 4 } + 5 p + 10$

Divide the polynomial by the monomial. $\frac { - 24 z ^ { 11 } - 72 z ^ { 15 } } { - 12 z ^ { 3 } }$

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. $- 9 x ( 4 - 9 x ) ( 4 + 9 x )$

Write the following number in standard decimal form. $( 4.03 ) \left( 10 ^ { 5 } \right)$

Find the product by using the shortcut pattern for multiplying binomials. $( 2 a + 9 ) ( a + 2 )$

Divide the monomials. $\frac { 2 y ^ { 5 } q ^ { 11 } } { y ^ { 3 } q ^ { 4 } }$

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

Perform the division and find the remainder. (16n2+32n−32)÷(4n+10)\left( 16 n ^ { 2 } + 32 n - 32 \right) \div ( 4 n + 10 )(16n2+32n−32)÷(4n+10)

Multiply. (8cd)(−7c5d)(−4d)( 8 c d ) \left( - 7 c ^ { 5 } d \right) ( - 4 d )(8cd)(−7c5d)(−4d)

Simplify the following algebraic expression and express your answer using positive exponents only. x8x−6x ^ { 8 } x ^ { - 6 }x8x−6

Add the polynomials. 5p2+4p+15 and −5p2−9p+105 p ^ { 2 } + 4 p + 15 \text { and } - 5 p ^ { 2 } - 9 p + 105p2+4p+15 and −5p2−9p+10

Perform the division of the polynomials by monomials. −96z6c7−96z12c10−12z3c4\frac { - 96 z ^ { 6 } c ^ { 7 } - 96 z ^ { 12 } c ^ { 10 } } { - 12 z ^ { 3 } c ^ { 4 } }−12z3c4−96z6c7−96z12c10​

Find the indicated product by applying the distributive property and combining similar terms. (x+8)(x2−6x−3)( x + 8 ) \left( x ^ { 2 } - 6 x - 3 \right)(x+8)(x2−6x−3)

Perform the division of the polynomials by monomials. −44z6−110z11−11z3\frac { - 44 z ^ { 6 } - 110 z ^ { 11 } } { - 11 z ^ { 3 } }−11z3−44z6−110z11​

Simplify the following algebraic expression and express your answer using positive exponents only. (7b−6)(2b9)\left( 7 b ^ { - 6 } \right) \left( 2 b ^ { 9 } \right)(7b−6)(2b9)

Simplify the following algebraic expression and express your answer using positive exponents only. b−4b6\frac { b ^ { - 4 } } { b ^ { 6 } }b6b−4​

Perform the division of the polynomials by monomials. 48p8d7+56p15d118p2d2\frac { 48 p ^ { 8 } d ^ { 7 } + 56 p ^ { 15 } d ^ { 11 } } { 8 p ^ { 2 } d ^ { 2 } }8p2d248p8d7+56p15d11​

Find the indicated product by applying the distributive property and combining similar terms. (3 x −-− 5) (3 x −-− 9)

Perform the indicated operations. (3z+3)−(8z−11)+(9z+3)( 3 z + 3 ) - ( 8 z - 11 ) + ( 9 z + 3 )(3z+3)−(8z−11)+(9z+3)

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. (2a3)2\left( 2 a ^ { 3 } \right) ^ { 2 }(2a3)2

When raising a power to a power, add exponents.

Subtract the polynomials using a horizontal format. 4p4−11p+2 from 2p4+5p+104 p ^ { 4 } - 11 p + 2 \text { from } 2 p ^ { 4 } + 5 p + 104p4−11p+2 from 2p4+5p+10

Divide the polynomial by the monomial. −24z11−72z15−12z3\frac { - 24 z ^ { 11 } - 72 z ^ { 15 } } { - 12 z ^ { 3 } }−12z3−24z11−72z15​

Write the following number in standard decimal form. (4.03)(105)( 4.03 ) \left( 10 ^ { 5 } \right)(4.03)(105)

Find the product by using the shortcut pattern for multiplying binomials. (2a+9)(a+2)( 2 a + 9 ) ( a + 2 )(2a+9)(a+2)

Divide the monomials. 2y5q11y3q4\frac { 2 y ^ { 5 } q ^ { 11 } } { y ^ { 3 } q ^ { 4 } }y3q42y5q11​

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 and find the remainder. $\left( 16 n ^ { 2 } + 32 n - 32 \right) \div ( 4 n + 10 )$

Multiply. $( 8 c d ) \left( - 7 c ^ { 5 } d \right) ( - 4 d )$

Simplify the following algebraic expression and express your answer using positive exponents only. $x ^ { 8 } x ^ { - 6 }$

Add the polynomials. $5 p ^ { 2 } + 4 p + 15 \text { and } - 5 p ^ { 2 } - 9 p + 10$

Perform the division of the polynomials by monomials. $\frac { - 96 z ^ { 6 } c ^ { 7 } - 96 z ^ { 12 } c ^ { 10 } } { - 12 z ^ { 3 } c ^ { 4 } }$

Find the indicated product by applying the distributive property and combining similar terms. $( x + 8 ) \left( x ^ { 2 } - 6 x - 3 \right)$

Perform the division of the polynomials by monomials. $\frac { - 44 z ^ { 6 } - 110 z ^ { 11 } } { - 11 z ^ { 3 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 7 b ^ { - 6 } \right) \left( 2 b ^ { 9 } \right)$

Simplify the following algebraic expression and express your answer using positive exponents only. $\frac { b ^ { - 4 } } { b ^ { 6 } }$

Perform the division of the polynomials by monomials. $\frac { 48 p ^ { 8 } d ^ { 7 } + 56 p ^ { 15 } d ^ { 11 } } { 8 p ^ { 2 } d ^ { 2 } }$

Find the indicated product by applying the distributive property and combining similar terms. (3 x $-$ 5) (3 x $-$ 9)

Perform the indicated operations. $( 3 z + 3 ) - ( 8 z - 11 ) + ( 9 z + 3 )$

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( 2 a ^ { 3 } \right) ^ { 2 }$

Subtract the polynomials using a horizontal format. $4 p ^ { 4 } - 11 p + 2 \text { from } 2 p ^ { 4 } + 5 p + 10$

Divide the polynomial by the monomial. $\frac { - 24 z ^ { 11 } - 72 z ^ { 15 } } { - 12 z ^ { 3 } }$

Write the following number in standard decimal form. $( 4.03 ) \left( 10 ^ { 5 } \right)$

Find the product by using the shortcut pattern for multiplying binomials. $( 2 a + 9 ) ( a + 2 )$

Divide the monomials. $\frac { 2 y ^ { 5 } q ^ { 11 } } { y ^ { 3 } q ^ { 4 } }$