Question 1

Perform the division. $\frac { 64 x ^ { 3 } - 27 } { 4 x - 3 }$

Accepted Answer

A)  $16 x ^ { 2 } + 12 x - 9$ 
B)  $16 x ^ { 2 } - 12 x - 9$ 
C)  $16 x ^ { 2 } + 12 x + 9$ 
D)  $16 x ^ { 2 } - 12 x + 9$ 
E)  $16 x ^ { 3 } + 12 x + 9$ 
A)  $16 x ^ { 2 } + 12 x - 9$ 
B)  $16 x ^ { 2 } - 12 x - 9$ 
C)  $16 x ^ { 2 } + 12 x + 9$ 
D)  $16 x ^ { 2 } - 12 x + 9$ 
E)  $16 x ^ { 3 } + 12 x + 9$

Question 2

Write the following number in standard decimal form. $( 6.11 ) \left( 10 ^ { 3 } \right)$

Accepted Answer

The answer of Write the following number in standard decimal...

Question 3

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

Accepted Answer

A)  $x ^ { 4 } + 3 x ^ { 3 } - 26 x ^ { 2 } + 6 x - 12$ 
B)  $x ^ { 4 } + 3 x ^ { 3 } - 26 x ^ { 2 } + 18 x + 12$ 
C)  $x ^ { 4 } + 3 x ^ { 3 } - 8 x ^ { 2 } + 12 x + 6$ 
D)  $x ^ { 4 } - 3 x ^ { 3 } - 24 x ^ { 2 } + 6 x + 12$ 
E)  $x ^ { 4 } + 3 x ^ { 3 } - 26 x ^ { 2 } + 6 x + 12$ 
A)  $x ^ { 4 } + 3 x ^ { 3 } - 26 x ^ { 2 } + 6 x - 12$ 
B)  $x ^ { 4 } + 3 x ^ { 3 } - 26 x ^ { 2 } + 18 x + 12$ 
C)  $x ^ { 4 } + 3 x ^ { 3 } - 8 x ^ { 2 } + 12 x + 6$ 
D)  $x ^ { 4 } - 3 x ^ { 3 } - 24 x ^ { 2 } + 6 x + 12$ 
E)  $x ^ { 4 } + 3 x ^ { 3 } - 26 x ^ { 2 } + 6 x + 12$

Question 4

Determine the degree of the polynomial. $4 y ^ { 3 } q ^ { 4 } + 8 y ^ { 3 } q$

Accepted Answer

The answer of Determine the degree of the polynomial. \(4...

Question 5

Remove the parentheses by multiplying and then simplify by combining similar terms. $9 ( x + 6 y ) + 9 ( 4 x + 5 y )$

Accepted Answer

A)  45 x + 104 y 
B)  44 x + 99 y 
C)  44 x + 104 y 
D)  47 x + 97 y 
E)  45 x + 99 y 
A)  45 x + 104 y 
B)  44 x + 99 y 
C)  44 x + 104 y 
D)  47 x + 97 y 
E)  45 x + 99 y

Question 6

Find the indicated products by using the shortcut pattern for multiplying binomials. (3 $-$ 8 x )(5 $-$ 9 x )

Accepted Answer

A)  $15 - 67 x + 72 x ^ { 2 }$ 
B)  $15 - 67 x + 8 x ^ { 2 }$ 
C)  $15 - 27 x - 72 x ^ { 2 }$ 
D)  $15 + 67 x + 72 x ^ { 2 }$ 
E)  $15 - 27 x + 72 x ^ { 2 }$ 
A)  $15 - 67 x + 72 x ^ { 2 }$ 
B)  $15 - 67 x + 8 x ^ { 2 }$ 
C)  $15 - 27 x - 72 x ^ { 2 }$ 
D)  $15 + 67 x + 72 x ^ { 2 }$ 
E)  $15 - 27 x + 72 x ^ { 2 }$

Question 7

Add the polynomials. $3 y + 11,8 y ^ { 5 } + 5 y + 10 \text { and } 9 y ^ { 5 } - 9 y + 10$

Accepted Answer

The answer of Add the polynomials. \(3 y + 11,8...

Question 8

Perform the division and find the remainder. $\frac { 1 + 2 y ^ { 2 } - 3 y } { y + 3 }$ Remainder: __________

Accepted Answer

The answer of Perform the division and find the remainder....

Question 9

Perform the indicated operations and simplify. $( 4 a ) ^ { 2 } \left( 2 a ^ { 4 } \right)$

Accepted Answer

The answer of Perform the indicated operations and simplify. \((...

Question 10

Find the indicated product by applying the distributive property and combining similar terms. $( x + 2 ) \left( x ^ { 2 } - 4 x - 5 \right)$

Accepted Answer

The answer of Find the indicated product by applying the...

Question 11

Evaluate the following numerical expression. $\frac { 2 ^ { 3 } } { 2 ^ { - 3 } }$

Accepted Answer

The answer of Evaluate the following numerical expression. \(\frac {...

Question 12

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 4 u ^ { 4 } b ^ { 3 } \right) ^ { - 1 }$

Accepted Answer

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

Question 13

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 4, b = 2 and c = 7.

Accepted Answer

A)  $5 x - 18$ 
B)  $10 x - 18$ 
C)  $10 x + 18$ 
D)  $180 x$ 
E)  $20 x + 36$ 
A)  $5 x - 18$ 
B)  $10 x - 18$ 
C)  $10 x + 18$ 
D)  $180 x$ 
E)  $20 x + 36$

Question 14

Represent the area of the shaded region in the following figure, where a = 7, b = 8, c = 3 and d = 9.

Accepted Answer

A)  $7 x ^ { 2 } + 5 x$ 
B)  $7 x ^ { 2 } - 5 x - 27$ 
C)  $7 x ^ { 2 } + 5 x + 27$ 
D)  $7 x ^ { 2 } - 5 x + 27$ 
E)  $7 x ^ { 2 } + 5 x - 27$ 
A)  $7 x ^ { 2 } + 5 x$ 
B)  $7 x ^ { 2 } - 5 x - 27$ 
C)  $7 x ^ { 2 } + 5 x + 27$ 
D)  $7 x ^ { 2 } - 5 x + 27$ 
E)  $7 x ^ { 2 } + 5 x - 27$

Question 15

Subtract the polynomials using a vertical format. $- 2 p - 4 \text { from } 4 p + 11$

Accepted Answer

A)  $- 6 p + 15$ 
B)  $- 6 p - 15$ 
C)  $6 p + 15$ 
D)  $6 p - 15$ 
A)  $- 6 p + 15$ 
B)  $- 6 p - 15$ 
C)  $6 p + 15$ 
D)  $6 p - 15$

Question 16

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( 4 b ^ { 4 } \right) ^ { 3 }$

Accepted Answer

A)  $4 b ^ { 7 }$ 
B)  $4 b ^ { 12 }$ 
C)  $64 b ^ { 7 }$ 
D)  $16 b ^ { 12 }$ 
E)  $64 b ^ { 12 }$ 
A)  $4 b ^ { 7 }$ 
B)  $4 b ^ { 12 }$ 
C)  $64 b ^ { 7 }$ 
D)  $16 b ^ { 12 }$ 
E)  $64 b ^ { 12 }$

Question 17

Divide the polynomial by the monomial. $\frac { - 30 p ^ { 8 } + 18 p ^ { 11 } - 18 p ^ { 15 } } { - 3 p ^ { 3 } }$

Accepted Answer

A)  $10 p ^ { 5 } - 6 p ^ { 9 } + 6 p ^ { 12 }$ 
B)  $10 p ^ { 6 } - 6 p ^ { 8 } + 6 p ^ { 13 }$ 
C)  $10 p ^ { 5 } - 6 p ^ { 9 } + 6 p ^ { 13 }$ 
D)  $10 p ^ { 5 } - 6 p ^ { 8 } + 6 p ^ { 12 }$ 
E)  $10 p ^ { 11 } - 6 p ^ { 14 } + 6 p ^ { 18 }$ 
A)  $10 p ^ { 5 } - 6 p ^ { 9 } + 6 p ^ { 12 }$ 
B)  $10 p ^ { 6 } - 6 p ^ { 8 } + 6 p ^ { 13 }$ 
C)  $10 p ^ { 5 } - 6 p ^ { 9 } + 6 p ^ { 13 }$ 
D)  $10 p ^ { 5 } - 6 p ^ { 8 } + 6 p ^ { 12 }$ 
E)  $10 p ^ { 11 } - 6 p ^ { 14 } + 6 p ^ { 18 }$

Question 18

Perform the indicated operations. $12 x - [ 6 x - ( 7 x - 4 ) ]$

Accepted Answer

A)  $- 13 x - 4$ 
B)  $13 x - 4$ 
C)  $13 x + 4$ 
A)  $- 13 x - 4$ 
B)  $13 x - 4$ 
C)  $13 x + 4$

Question 19

Divide the monomials. $\frac { 7 x r } { - x r }$

Accepted Answer

A)  $7 x ^ { 2 } r ^ { 2 }$ 
B)  $x ^ { 2 } r ^ { 2 }$ 
C)  $7 \times r$ 
D)  $- 7$ 
E)  $- 7 x r$ 
A)  $7 x ^ { 2 } r ^ { 2 }$ 
B)  $x ^ { 2 } r ^ { 2 }$ 
C)  $7 \times r$ 
D)  $- 7$ 
E)  $- 7 x r$

Question 20

Find the indicated product by applying the distributive property and combining similar terms. ( n $-$ 5) ( n $-$ 6)

Accepted Answer

The answer of Find the indicated product by applying the...

Perform the division. $\frac { 64 x ^ { 3 } - 27 } { 4 x - 3 }$

Write the following number in standard decimal form. $( 6.11 ) \left( 10 ^ { 3 } \right)$

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

Determine the degree of the polynomial. $4 y ^ { 3 } q ^ { 4 } + 8 y ^ { 3 } q$

Remove the parentheses by multiplying and then simplify by combining similar terms. $9 ( x + 6 y ) + 9 ( 4 x + 5 y )$

Find the indicated products by using the shortcut pattern for multiplying binomials. (3 $-$ 8 x )(5 $-$ 9 x )

Add the polynomials. $3 y + 11,8 y ^ { 5 } + 5 y + 10 \text { and } 9 y ^ { 5 } - 9 y + 10$

Perform the division and find the remainder. $\frac { 1 + 2 y ^ { 2 } - 3 y } { y + 3 }$ Remainder: __________

Perform the indicated operations and simplify. $( 4 a ) ^ { 2 } \left( 2 a ^ { 4 } \right)$

Find the indicated product by applying the distributive property and combining similar terms. $( x + 2 ) \left( x ^ { 2 } - 4 x - 5 \right)$

Evaluate the following numerical expression. $\frac { 2 ^ { 3 } } { 2 ^ { - 3 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 4 u ^ { 4 } b ^ { 3 } \right) ^ { - 1 }$

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 4, b = 2 and c = 7.

Represent the area of the shaded region in the following figure, where a = 7, b = 8, c = 3 and d = 9.

Subtract the polynomials using a vertical format. $- 2 p - 4 \text { from } 4 p + 11$

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( 4 b ^ { 4 } \right) ^ { 3 }$

Divide the polynomial by the monomial. $\frac { - 30 p ^ { 8 } + 18 p ^ { 11 } - 18 p ^ { 15 } } { - 3 p ^ { 3 } }$

Perform the indicated operations. $12 x - [ 6 x - ( 7 x - 4 ) ]$

Divide the monomials. $\frac { 7 x r } { - x r }$

Find the indicated product by applying the distributive property and combining similar terms. ( n $-$ 5) ( n $-$ 6)

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. 64x3−274x−3\frac { 64 x ^ { 3 } - 27 } { 4 x - 3 }4x−364x3−27​

Write the following number in standard decimal form. (6.11)(103)( 6.11 ) \left( 10 ^ { 3 } \right)(6.11)(103)

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

Determine the degree of the polynomial. 4y3q4+8y3q4 y ^ { 3 } q ^ { 4 } + 8 y ^ { 3 } q4y3q4+8y3q

Remove the parentheses by multiplying and then simplify by combining similar terms. 9(x+6y)+9(4x+5y)9 ( x + 6 y ) + 9 ( 4 x + 5 y )9(x+6y)+9(4x+5y)

Find the indicated products by using the shortcut pattern for multiplying binomials. (3 −-− 8 x )(5 −-− 9 x )

Add the polynomials. 3y+11,8y5+5y+10 and 9y5−9y+103 y + 11,8 y ^ { 5 } + 5 y + 10 \text { and } 9 y ^ { 5 } - 9 y + 103y+11,8y5+5y+10 and 9y5−9y+10

Perform the division and find the remainder. 1+2y2−3yy+3\frac { 1 + 2 y ^ { 2 } - 3 y } { y + 3 }y+31+2y2−3y​ Remainder: __________

Perform the indicated operations and simplify. (4a)2(2a4)( 4 a ) ^ { 2 } \left( 2 a ^ { 4 } \right)(4a)2(2a4)

Find the indicated product by applying the distributive property and combining similar terms. (x+2)(x2−4x−5)( x + 2 ) \left( x ^ { 2 } - 4 x - 5 \right)(x+2)(x2−4x−5)

Evaluate the following numerical expression. 232−3\frac { 2 ^ { 3 } } { 2 ^ { - 3 } }2−323​

Simplify the following algebraic expression and express your answer using positive exponents only. (4u4b3)−1\left( 4 u ^ { 4 } b ^ { 3 } \right) ^ { - 1 }(4u4b3)−1

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 4, b = 2 and c = 7.

Represent the area of the shaded region in the following figure, where a = 7, b = 8, c = 3 and d = 9.

Subtract the polynomials using a vertical format. −2p−4 from 4p+11- 2 p - 4 \text { from } 4 p + 11−2p−4 from 4p+11

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. (4b4)3\left( 4 b ^ { 4 } \right) ^ { 3 }(4b4)3

Divide the polynomial by the monomial. −30p8+18p11−18p15−3p3\frac { - 30 p ^ { 8 } + 18 p ^ { 11 } - 18 p ^ { 15 } } { - 3 p ^ { 3 } }−3p3−30p8+18p11−18p15​

Perform the indicated operations. 12x−[6x−(7x−4)]12 x - [ 6 x - ( 7 x - 4 ) ]12x−[6x−(7x−4)]

Divide the monomials. 7xr−xr\frac { 7 x r } { - x r }−xr7xr​

Find the indicated product by applying the distributive property and combining similar terms. ( n −-− 5) ( n −-− 6)

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. $\frac { 64 x ^ { 3 } - 27 } { 4 x - 3 }$

Write the following number in standard decimal form. $( 6.11 ) \left( 10 ^ { 3 } \right)$

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

Determine the degree of the polynomial. $4 y ^ { 3 } q ^ { 4 } + 8 y ^ { 3 } q$

Remove the parentheses by multiplying and then simplify by combining similar terms. $9 ( x + 6 y ) + 9 ( 4 x + 5 y )$

Find the indicated products by using the shortcut pattern for multiplying binomials. (3 $-$ 8 x )(5 $-$ 9 x )

Add the polynomials. $3 y + 11,8 y ^ { 5 } + 5 y + 10 \text { and } 9 y ^ { 5 } - 9 y + 10$

Perform the division and find the remainder. $\frac { 1 + 2 y ^ { 2 } - 3 y } { y + 3 }$ Remainder: __________

Perform the indicated operations and simplify. $( 4 a ) ^ { 2 } \left( 2 a ^ { 4 } \right)$

Find the indicated product by applying the distributive property and combining similar terms. $( x + 2 ) \left( x ^ { 2 } - 4 x - 5 \right)$

Evaluate the following numerical expression. $\frac { 2 ^ { 3 } } { 2 ^ { - 3 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 4 u ^ { 4 } b ^ { 3 } \right) ^ { - 1 }$

Subtract the polynomials using a vertical format. $- 2 p - 4 \text { from } 4 p + 11$

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( 4 b ^ { 4 } \right) ^ { 3 }$

Divide the polynomial by the monomial. $\frac { - 30 p ^ { 8 } + 18 p ^ { 11 } - 18 p ^ { 15 } } { - 3 p ^ { 3 } }$

Perform the indicated operations. $12 x - [ 6 x - ( 7 x - 4 ) ]$

Divide the monomials. $\frac { 7 x r } { - x r }$

Find the indicated product by applying the distributive property and combining similar terms. ( n $-$ 5) ( n $-$ 6)