Question 1

Find the indicated products by using the shortcut pattern for multiplying binomials. (5 x + 6)(7 x $-$ 5)

Accepted Answer

A)  $35 x ^ { 2 } + 17 x - 30$ 
B)  $35 x ^ { 2 } + 42 x - 30$ 
C)  $35 x ^ { 2 } + 17 x - 6$ 
D)  $5 x ^ { 2 } + 17 x - 30$ 
E)  none of these 
A)  $35 x ^ { 2 } + 17 x - 30$ 
B)  $35 x ^ { 2 } + 42 x - 30$ 
C)  $35 x ^ { 2 } + 17 x - 6$ 
D)  $5 x ^ { 2 } + 17 x - 30$ 
E)  none of these

Question 2

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. $( 3 x + 9 y ) ^ { 2 }$

Accepted Answer

The answer of Use one of the appropriate patterns \((...

Question 3

A trinomial has three terms, a binomial has two terms, and a monomial has one term.

Accepted Answer

A) True 
 B)False

Question 4

Simplify the following algebraic expression and express your answer using positive exponents only. $u ^ { - 7 } u ^ { - 6 }$

Accepted Answer

A)  $u ^ { 13 }$ 
B)  $\frac { 1 } { u ^ { 13 } }$ 
C)  $\frac { 1 } { u ^ { 42 } }$ 
A)  $u ^ { 13 }$ 
B)  $\frac { 1 } { u ^ { 13 } }$ 
C)  $\frac { 1 } { u ^ { 42 } }$

Question 5

Subtract the polynomials using a horizontal format. $- 4 z ^ { 3 } - 11 z ^ { 2 } + 2 \text { from } 8 z ^ { 3 } + 3 z ^ { 2 } + 10$

Accepted Answer

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

Question 6

Multiply the following. $\left( - 9 x ^ { 5 } b ^ { 5 } \right) ( 8 x b )$

Accepted Answer

A)  $- 69 x ^ { 6 } b ^ { 6 }$ 
B)  $- 74 x ^ { 6 } b ^ { 5 }$ 
C)  $- 72 x ^ { 5 } b ^ { 6 }$ 
D)  $- 72 x ^ { 6 } b ^ { 6 }$ 
A)  $- 69 x ^ { 6 } b ^ { 6 }$ 
B)  $- 74 x ^ { 6 } b ^ { 5 }$ 
C)  $- 72 x ^ { 5 } b ^ { 6 }$ 
D)  $- 72 x ^ { 6 } b ^ { 6 }$

Question 7

Find the indicated products by using the shortcut pattern for multiplying binomials. (9 x + 1) (8 x $-$ 5)

Accepted Answer

The answer of Find the indicated products by using the...

Question 8

Divide the polynomial by the monomial. $\frac { - 132 x ^ { 11 } c ^ { 8 } - 120 x ^ { 13 } c ^ { 14 } } { - 12 x ^ { 2 } c ^ { 3 } }$

Accepted Answer

A)  $11 x ^ { 9 } c ^ { 5 } + 10 x ^ { 12 } c ^ { 12 }$ 
B)  $11 x ^ { 9 } c ^ { 5 } + 10 x ^ { 11 } c ^ { 11 }$ 
C)  $11 x ^ { 10 } c ^ { 4 } + 10 x ^ { 11 } c ^ { 11 }$ 
D)  $11 x ^ { 9 } c ^ { 5 } + 10 x ^ { 11 } c ^ { 12 }$ 
E)  $11 x ^ { 9 } c ^ { 5 } - 10 x ^ { 12 } c ^ { 11 }$ 
A)  $11 x ^ { 9 } c ^ { 5 } + 10 x ^ { 12 } c ^ { 12 }$ 
B)  $11 x ^ { 9 } c ^ { 5 } + 10 x ^ { 11 } c ^ { 11 }$ 
C)  $11 x ^ { 10 } c ^ { 4 } + 10 x ^ { 11 } c ^ { 11 }$ 
D)  $11 x ^ { 9 } c ^ { 5 } + 10 x ^ { 11 } c ^ { 12 }$ 
E)  $11 x ^ { 9 } c ^ { 5 } - 10 x ^ { 12 } c ^ { 11 }$

Question 9

Divide the monomials. $\frac { - 24 x ^ { 11 } m ^ { 13 } } { 6 x ^ { 2 } m ^ { 4 } }$

Accepted Answer

A)  $4 x ^ { 10 } m ^ { 9 }$ 
B)  $- 4 x ^ { 9 } m ^ { 9 }$ 
C)  $- 4 x ^ { 11 } m ^ { 10 }$ 
D)  $- 4 x ^ { 9 } m ^ { 11 }$ 
E)  $4 x ^ { 9 } m ^ { 9 }$ 
A)  $4 x ^ { 10 } m ^ { 9 }$ 
B)  $- 4 x ^ { 9 } m ^ { 9 }$ 
C)  $- 4 x ^ { 11 } m ^ { 10 }$ 
D)  $- 4 x ^ { 9 } m ^ { 11 }$ 
E)  $4 x ^ { 9 } m ^ { 9 }$

Question 10

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. $( x + 4 ) ^ { 2 }$

Accepted Answer

A)  $x ^ { 2 } + 8 x + 16$ 
B)  $x ^ { 2 } + 8 x + 4$ 
C)  $x ^ { 2 } - 8 x + 16$ 
D)  $x ^ { 2 } + 4 x + 16$ 
E)  none of these 
A)  $x ^ { 2 } + 8 x + 16$ 
B)  $x ^ { 2 } + 8 x + 4$ 
C)  $x ^ { 2 } - 8 x + 16$ 
D)  $x ^ { 2 } + 4 x + 16$ 
E)  none of these

Question 11

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( \frac { 10 v ^ { 10 } } { 2 v ^ { - 5 } } \right) ^ { - 1 }$

Accepted Answer

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

Question 12

Determine the degree of the polynomial. $10 z ^ { 3 } l ^ { 5 } + 5 z ^ { 3 } l$

Accepted Answer

A)  15 
B)  8 
C)  5 
D)  3 
A)  15 
B)  8 
C)  5 
D)  3

Question 13

Evaluate the numerical expression. $\left( \frac { 5 ^ { - 1 } } { 6 } \right) ^ { - 2 }$

Accepted Answer

A)  908 
B)  904 
C)  900 
D)  912 
E)  916 
A)  908 
B)  904 
C)  900 
D)  912 
E)  916

Question 14

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( - 5 a ^ { 2 } b ^ { 7 } \right) ^ { 3 }$ Enter your answer as $k a ^ { p } b ^ { q }$ where k , p , q are numbers and a , b are variables.

Accepted Answer

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

Question 15

Divide the polynomial by the monomial. $\frac { 40 y ^ { 5 } a ^ { 15 } - 48 y ^ { 15 } a ^ { 13 } - 40 y ^ { 17 } a ^ { 17 } } { - 8 y ^ { 2 } a ^ { 2 } }$

Accepted Answer

A)  $- 5 y ^ { 3 } a ^ { 13 } + 11 y ^ { 28 } a ^ { 26 }$ 
B)  $5 y ^ { 3 } a ^ { 13 } + 6 y ^ { 13 } a ^ { 11 } + 5 y ^ { 15 } a ^ { 15 }$ 
C)  $- 11 y ^ { 3 } a ^ { 13 } + 6 y ^ { 13 } a ^ { 11 } + 5 y ^ { 15 } a ^ { 15 }$ 
D)  $- 5 y ^ { 3 } a ^ { 13 } + 6 y ^ { 13 } a ^ { 14 } + 5 y ^ { 28 } a ^ { 30 }$ 
E)  $- 5 y ^ { 3 } a ^ { 13 } + 6 y ^ { 13 } a ^ { 11 } + 5 y ^ { 15 } a ^ { 15 }$ 
A)  $- 5 y ^ { 3 } a ^ { 13 } + 11 y ^ { 28 } a ^ { 26 }$ 
B)  $5 y ^ { 3 } a ^ { 13 } + 6 y ^ { 13 } a ^ { 11 } + 5 y ^ { 15 } a ^ { 15 }$ 
C)  $- 11 y ^ { 3 } a ^ { 13 } + 6 y ^ { 13 } a ^ { 11 } + 5 y ^ { 15 } a ^ { 15 }$ 
D)  $- 5 y ^ { 3 } a ^ { 13 } + 6 y ^ { 13 } a ^ { 14 } + 5 y ^ { 28 } a ^ { 30 }$ 
E)  $- 5 y ^ { 3 } a ^ { 13 } + 6 y ^ { 13 } a ^ { 11 } + 5 y ^ { 15 } a ^ { 15 }$

Question 16

Evaluate the numerical expression. $5 ^ { - 3 } \cdot 5 ^ { 5 }$

Accepted Answer

A)  $- \frac { 1 } { 25 }$ 
B)  $25$ 
C)  $\frac { 1 } { 25 }$ 
D)  $125$ 
E)  $\frac { 1 } { 125 }$ 
A)  $- \frac { 1 } { 25 }$ 
B)  $25$ 
C)  $\frac { 1 } { 25 }$ 
D)  $125$ 
E)  $\frac { 1 } { 125 }$

Question 17

Perform the division of the polynomials by monomials. $\frac { - 81 z ^ { 12 } d ^ { 11 } - 54 z ^ { 11 } d ^ { 10 } } { - 9 z ^ { 4 } d ^ { 3 } }$

Accepted Answer

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

Question 18

Perform the indicated operations and simplify. $\left( - 3 x ^ { 3 } y ^ { 3 } \right) ^ { 3 } \left( - x y ^ { 5 } \right) ^ { 5 }$ Enter your answer as $k x ^ { p } y ^ { q }$ where k , p , q are numbers and x , y are variables.

Accepted Answer

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

Question 19

Divide the polynomial by the monomial. $\frac { - 30 y ^ { 7 } + 36 y ^ { 15 } - 66 y ^ { 10 } } { - 6 y ^ { 4 } }$

Accepted Answer

The answer of Divide the polynomial by the monomial. \(\frac...

Question 20

Perform the division of the polynomials by monomials. $\frac { 24 y ^ { 12 } d ^ { 14 } - 30 y ^ { 15 } d ^ { 15 } - 54 y ^ { 17 } d ^ { 17 } } { - 6 y ^ { 4 } d ^ { 4 } }$

Accepted Answer

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

Find the indicated products by using the shortcut pattern for multiplying binomials. (5 x + 6)(7 x $-$ 5)

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. $( 3 x + 9 y ) ^ { 2 }$

A trinomial has three terms, a binomial has two terms, and a monomial has one term.

Simplify the following algebraic expression and express your answer using positive exponents only. $u ^ { - 7 } u ^ { - 6 }$

Subtract the polynomials using a horizontal format. $- 4 z ^ { 3 } - 11 z ^ { 2 } + 2 \text { from } 8 z ^ { 3 } + 3 z ^ { 2 } + 10$

Multiply the following. $\left( - 9 x ^ { 5 } b ^ { 5 } \right) ( 8 x b )$

Find the indicated products by using the shortcut pattern for multiplying binomials. (9 x + 1) (8 x $-$ 5)

Divide the polynomial by the monomial. $\frac { - 132 x ^ { 11 } c ^ { 8 } - 120 x ^ { 13 } c ^ { 14 } } { - 12 x ^ { 2 } c ^ { 3 } }$

Divide the monomials. $\frac { - 24 x ^ { 11 } m ^ { 13 } } { 6 x ^ { 2 } m ^ { 4 } }$

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. $( x + 4 ) ^ { 2 }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( \frac { 10 v ^ { 10 } } { 2 v ^ { - 5 } } \right) ^ { - 1 }$

Determine the degree of the polynomial. $10 z ^ { 3 } l ^ { 5 } + 5 z ^ { 3 } l$

Evaluate the numerical expression. $\left( \frac { 5 ^ { - 1 } } { 6 } \right) ^ { - 2 }$

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( - 5 a ^ { 2 } b ^ { 7 } \right) ^ { 3 }$ Enter your answer as $k a ^ { p } b ^ { q }$ where k , p , q are numbers and a , b are variables.

Divide the polynomial by the monomial. $\frac { 40 y ^ { 5 } a ^ { 15 } - 48 y ^ { 15 } a ^ { 13 } - 40 y ^ { 17 } a ^ { 17 } } { - 8 y ^ { 2 } a ^ { 2 } }$

Evaluate the numerical expression. $5 ^ { - 3 } \cdot 5 ^ { 5 }$

Perform the division of the polynomials by monomials. $\frac { - 81 z ^ { 12 } d ^ { 11 } - 54 z ^ { 11 } d ^ { 10 } } { - 9 z ^ { 4 } d ^ { 3 } }$

Perform the indicated operations and simplify. $\left( - 3 x ^ { 3 } y ^ { 3 } \right) ^ { 3 } \left( - x y ^ { 5 } \right) ^ { 5 }$ Enter your answer as $k x ^ { p } y ^ { q }$ where k , p , q are numbers and x , y are variables.

Divide the polynomial by the monomial. $\frac { - 30 y ^ { 7 } + 36 y ^ { 15 } - 66 y ^ { 10 } } { - 6 y ^ { 4 } }$

Perform the division of the polynomials by monomials. $\frac { 24 y ^ { 12 } d ^ { 14 } - 30 y ^ { 15 } d ^ { 15 } - 54 y ^ { 17 } d ^ { 17 } } { - 6 y ^ { 4 } d ^ { 4 } }$

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

Find the indicated products by using the shortcut pattern for multiplying binomials. (5 x + 6)(7 x −-− 5)

A trinomial has three terms, a binomial has two terms, and a monomial has one term.

Simplify the following algebraic expression and express your answer using positive exponents only. u−7u−6u ^ { - 7 } u ^ { - 6 }u−7u−6

Subtract the polynomials using a horizontal format. −4z3−11z2+2 from 8z3+3z2+10- 4 z ^ { 3 } - 11 z ^ { 2 } + 2 \text { from } 8 z ^ { 3 } + 3 z ^ { 2 } + 10−4z3−11z2+2 from 8z3+3z2+10

Multiply the following. (−9x5b5)(8xb)\left( - 9 x ^ { 5 } b ^ { 5 } \right) ( 8 x b )(−9x5b5)(8xb)

Find the indicated products by using the shortcut pattern for multiplying binomials. (9 x + 1) (8 x −-− 5)

Divide the polynomial by the monomial. −132x11c8−120x13c14−12x2c3\frac { - 132 x ^ { 11 } c ^ { 8 } - 120 x ^ { 13 } c ^ { 14 } } { - 12 x ^ { 2 } c ^ { 3 } }−12x2c3−132x11c8−120x13c14​

Divide the monomials. −24x11m136x2m4\frac { - 24 x ^ { 11 } m ^ { 13 } } { 6 x ^ { 2 } m ^ { 4 } }6x2m4−24x11m13​

Simplify the following algebraic expression and express your answer using positive exponents only. (10v102v−5)−1\left( \frac { 10 v ^ { 10 } } { 2 v ^ { - 5 } } \right) ^ { - 1 }(2v−510v10​)−1

Determine the degree of the polynomial. 10z3l5+5z3l10 z ^ { 3 } l ^ { 5 } + 5 z ^ { 3 } l10z3l5+5z3l

Evaluate the numerical expression. (5−16)−2\left( \frac { 5 ^ { - 1 } } { 6 } \right) ^ { - 2 }(65−1​)−2

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. (−5a2b7)3\left( - 5 a ^ { 2 } b ^ { 7 } \right) ^ { 3 }(−5a2b7)3 Enter your answer as kapbqk a ^ { p } b ^ { q }kapbq where k , p , q are numbers and a , b are variables.

Divide the polynomial by the monomial. 40y5a15−48y15a13−40y17a17−8y2a2\frac { 40 y ^ { 5 } a ^ { 15 } - 48 y ^ { 15 } a ^ { 13 } - 40 y ^ { 17 } a ^ { 17 } } { - 8 y ^ { 2 } a ^ { 2 } }−8y2a240y5a15−48y15a13−40y17a17​

Evaluate the numerical expression. 5−3⋅555 ^ { - 3 } \cdot 5 ^ { 5 }5−3⋅55

Perform the division of the polynomials by monomials. −81z12d11−54z11d10−9z4d3\frac { - 81 z ^ { 12 } d ^ { 11 } - 54 z ^ { 11 } d ^ { 10 } } { - 9 z ^ { 4 } d ^ { 3 } }−9z4d3−81z12d11−54z11d10​

Perform the indicated operations and simplify. (−3x3y3)3(−xy5)5\left( - 3 x ^ { 3 } y ^ { 3 } \right) ^ { 3 } \left( - x y ^ { 5 } \right) ^ { 5 }(−3x3y3)3(−xy5)5 Enter your answer as kxpyqk x ^ { p } y ^ { q }kxpyq where k , p , q are numbers and x , y are variables.

Divide the polynomial by the monomial. −30y7+36y15−66y10−6y4\frac { - 30 y ^ { 7 } + 36 y ^ { 15 } - 66 y ^ { 10 } } { - 6 y ^ { 4 } }−6y4−30y7+36y15−66y10​

Perform the division of the polynomials by monomials. 24y12d14−30y15d15−54y17d17−6y4d4\frac { 24 y ^ { 12 } d ^ { 14 } - 30 y ^ { 15 } d ^ { 15 } - 54 y ^ { 17 } d ^ { 17 } } { - 6 y ^ { 4 } d ^ { 4 } }−6y4d424y12d14−30y15d15−54y17d17​

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

Find the indicated products by using the shortcut pattern for multiplying binomials. (5 x + 6)(7 x $-$ 5)

Simplify the following algebraic expression and express your answer using positive exponents only. $u ^ { - 7 } u ^ { - 6 }$

Subtract the polynomials using a horizontal format. $- 4 z ^ { 3 } - 11 z ^ { 2 } + 2 \text { from } 8 z ^ { 3 } + 3 z ^ { 2 } + 10$

Multiply the following. $\left( - 9 x ^ { 5 } b ^ { 5 } \right) ( 8 x b )$

Find the indicated products by using the shortcut pattern for multiplying binomials. (9 x + 1) (8 x $-$ 5)

Divide the polynomial by the monomial. $\frac { - 132 x ^ { 11 } c ^ { 8 } - 120 x ^ { 13 } c ^ { 14 } } { - 12 x ^ { 2 } c ^ { 3 } }$

Divide the monomials. $\frac { - 24 x ^ { 11 } m ^ { 13 } } { 6 x ^ { 2 } m ^ { 4 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( \frac { 10 v ^ { 10 } } { 2 v ^ { - 5 } } \right) ^ { - 1 }$

Determine the degree of the polynomial. $10 z ^ { 3 } l ^ { 5 } + 5 z ^ { 3 } l$

Evaluate the numerical expression. $\left( \frac { 5 ^ { - 1 } } { 6 } \right) ^ { - 2 }$

Raise the monomial to the indicated power. Use the properties of exponents to help with the manipulation. $\left( - 5 a ^ { 2 } b ^ { 7 } \right) ^ { 3 }$ Enter your answer as $k a ^ { p } b ^ { q }$ where k , p , q are numbers and a , b are variables.

Divide the polynomial by the monomial. $\frac { 40 y ^ { 5 } a ^ { 15 } - 48 y ^ { 15 } a ^ { 13 } - 40 y ^ { 17 } a ^ { 17 } } { - 8 y ^ { 2 } a ^ { 2 } }$

Evaluate the numerical expression. $5 ^ { - 3 } \cdot 5 ^ { 5 }$

Perform the division of the polynomials by monomials. $\frac { - 81 z ^ { 12 } d ^ { 11 } - 54 z ^ { 11 } d ^ { 10 } } { - 9 z ^ { 4 } d ^ { 3 } }$

Perform the indicated operations and simplify. $\left( - 3 x ^ { 3 } y ^ { 3 } \right) ^ { 3 } \left( - x y ^ { 5 } \right) ^ { 5 }$ Enter your answer as $k x ^ { p } y ^ { q }$ where k , p , q are numbers and x , y are variables.

Divide the polynomial by the monomial. $\frac { - 30 y ^ { 7 } + 36 y ^ { 15 } - 66 y ^ { 10 } } { - 6 y ^ { 4 } }$

Perform the division of the polynomials by monomials. $\frac { 24 y ^ { 12 } d ^ { 14 } - 30 y ^ { 15 } d ^ { 15 } - 54 y ^ { 17 } d ^ { 17 } } { - 6 y ^ { 4 } d ^ { 4 } }$