Question 1

Find the indicated product by using the shortcut pattern for multiplying binomials. ( x + 3)( x + 9)

Accepted Answer

A)  $x ^ { 2 } + 27 x$ 
B)  $x ^ { 2 } + 9 x + 27$ 
C)  $x ^ { 2 } + 12 x + 27$ 
D)  $13 x ^ { 2 } + 27$ 
E)  none of these 
A)  $x ^ { 2 } + 27 x$ 
B)  $x ^ { 2 } + 9 x + 27$ 
C)  $x ^ { 2 } + 12 x + 27$ 
D)  $13 x ^ { 2 } + 27$ 
E)  none of these

Question 2

Divide the monomials. $\frac { 6 p w } { - p w }$

Accepted Answer

The answer of Divide the monomials. \(\frac { 6 p...

Question 3

Find the indicated product by applying the distributive property. ( x $-$ 9)( y $-$ 8)

Accepted Answer

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

Question 4

Perform the division and find the quotient. $\left( 10 y ^ { 2 } + 49 y + 49 \right) \div ( 2 y + 7 )$

Accepted Answer

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

Question 5

Add the polynomials. $2 x + 9 \text { and } 11 x + 5$

Accepted Answer

The answer of Add the polynomials. \(2 x + 9...

Question 6

A square piece of cardboard is y = 15 inches long on each side. From each corner a square piece x inches on a side is cut out as shown. The flaps are then turned up to form an open box. Find a polynomial that represents the volume of the box.

Accepted Answer

A)  $225 x - 60 x ^ { 2 } + x ^ { 3 }$ 
B)  $225 - 60 x + 4 x ^ { 2 }$ 
C)  $225 x - 60 x ^ { 2 } + 4 x ^ { 3 }$ 
D)  $225 x - 15 x ^ { 2 } + 4 x ^ { 3 }$ 
E)  none of these 
A)  $225 x - 60 x ^ { 2 } + x ^ { 3 }$ 
B)  $225 - 60 x + 4 x ^ { 2 }$ 
C)  $225 x - 60 x ^ { 2 } + 4 x ^ { 3 }$ 
D)  $225 x - 15 x ^ { 2 } + 4 x ^ { 3 }$ 
E)  none of these

Question 7

Multiply the following. $\left( - 6 a ^ { 3 } y ^ { 4 } \right) ( 12 a y )$ Enter your answer as $k a ^ { p } y ^ { q }$ where k , p , q are numbers and a , y are variables.

Accepted Answer

The answer of Multiply the following. \(\left( - 6 a...

Question 8

Find the product. $\left( x ^ { 4 n } \right) \left( x ^ { 5 n } \right)$ Assume that the variables in the exponents represent positive integers; for example, $\left( x ^ { 2 n } \right) \left( x ^ { 4 n } \right) = x ^ { 2 n + 4 n } = x ^ { 6 n }$ .

Accepted Answer

A)  $x ^ { 7 n }$ 
B)  $x ^ { 6 n }$ 
C)  $x ^ { 9 n }$ 
D)  $x ^ { 5 n }$ 
E)  $x ^ { 2 n }$ 
A)  $x ^ { 7 n }$ 
B)  $x ^ { 6 n }$ 
C)  $x ^ { 9 n }$ 
D)  $x ^ { 5 n }$ 
E)  $x ^ { 2 n }$

Question 9

Perform the division. $\frac { 8 n ^ { 3 } - 27 } { 2 n - 3 }$

Accepted Answer

A)  $4 n ^ { 2 } + 6 n + 9$ 
B)  $4 n ^ { 2 } - 6 n - 9$ 
C)  $4 n ^ { 2 } + 6 n - 9$ 
D)  $4 n ^ { 2 } - 6 n + 9$ 
A)  $4 n ^ { 2 } + 6 n + 9$ 
B)  $4 n ^ { 2 } - 6 n - 9$ 
C)  $4 n ^ { 2 } + 6 n - 9$ 
D)  $4 n ^ { 2 } - 6 n + 9$

Question 10

Perform the division. $\left( 6 y ^ { 3 } - y ^ { 2 } - 16 y - 12 \right) \div ( y - 2 )$

Accepted Answer

The answer of Perform the division. \(\left( 6 y ^...

Question 11

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 9 y ^ { - 3 } \right) \left( 10 y ^ { 8 } \right)$

Accepted Answer

A)  $19 y ^ { 5 }$ 
B)  $19 y ^ { 11 }$ 
C)  $90 y ^ { 5 }$ 
D)  $90 y ^ { 11 }$ 
A)  $19 y ^ { 5 }$ 
B)  $19 y ^ { 11 }$ 
C)  $90 y ^ { 5 }$ 
D)  $90 y ^ { 11 }$

Question 12

Write the following number in scientific notation. 649

Accepted Answer

A)  $0.649 \cdot 10 ^ { 4 }$ 
B)  $6.49 \cdot 10 ^ { 2 }$ 
C)  $64.9 \cdot 10 ^ { 2 }$ 
A)  $0.649 \cdot 10 ^ { 4 }$ 
B)  $6.49 \cdot 10 ^ { 2 }$ 
C)  $64.9 \cdot 10 ^ { 2 }$

Question 13

Find $( x + 5 ) ^ { 3 }$ . Don t forget that $( x + 5 ) ^ { 3 }$ means ( x + 5)( x + 5)( x + 5).

Accepted Answer

The answer of Find \(( x + 5 ) ^...

Question 14

Perform the indicated operations and simplify. $( 5 x ) ^ { 3 } \left( 4 x ^ { 3 } \right)$

Accepted Answer

A)  $507 x ^ { 6 }$ 
B)  $500 x ^ { 10 }$ 
C)  $502 x ^ { 9 }$ 
D)  $500 x ^ { 6 }$ 
E)  $505 x ^ { 6 }$ 
A)  $507 x ^ { 6 }$ 
B)  $500 x ^ { 10 }$ 
C)  $502 x ^ { 9 }$ 
D)  $500 x ^ { 6 }$ 
E)  $505 x ^ { 6 }$

Question 15

Simplify the following algebraic expression and express your answer using positive exponents only. $b ^ { - 1 } b ^ { - 4 }$

Accepted Answer

A)  $\frac { 1 } { b ^ { 5 } }$ 
B)  $b ^ { - 5 }$ 
C)  $b ^ { 5 }$ 
D)  $\frac { 1 } { b ^ { 7 } }$ 
E)  $\frac { 1 } { b ^ { - 3 } }$ 
A)  $\frac { 1 } { b ^ { 5 } }$ 
B)  $b ^ { - 5 }$ 
C)  $b ^ { 5 }$ 
D)  $\frac { 1 } { b ^ { 7 } }$ 
E)  $\frac { 1 } { b ^ { - 3 } }$

Question 16

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( a ^ { - 5 } b ^ { - 2 } \right) ^ { 4 }$

Accepted Answer

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

Question 17

Perform the division and find the quotient. Answer does not include the remainder. $\frac { 5 y ^ { 3 } + 21 y ^ { 2 } - 17 y + 8 } { y + 5 }$

Accepted Answer

A)  $4 y ^ { 2 } + 5 y - 3$ 
B)  $5 y ^ { 2 } - 4 y + 3$ 
C)  $5 y ^ { 2 } + 4 y + 3$ 
D)  $4 y ^ { 2 } - 5 y + 3$ 
E)  $5 y ^ { 2 } + 4 y - 3$ 
A)  $4 y ^ { 2 } + 5 y - 3$ 
B)  $5 y ^ { 2 } - 4 y + 3$ 
C)  $5 y ^ { 2 } + 4 y + 3$ 
D)  $4 y ^ { 2 } - 5 y + 3$ 
E)  $5 y ^ { 2 } + 4 y - 3$

Question 18

Remove the parentheses by multiplying and then simplify by combining similar terms. $6 ( x + 8 y ) + 3 ( 3 x + 7 y )$

Accepted Answer

The answer of Remove the parentheses by multiplying and then...

Question 19

Divide the monomials. $\frac { - 10 x ^ { 9 } q ^ { 11 } } { 5 x ^ { 2 } q ^ { 2 } }$

Accepted Answer

A)  $- 2 x ^ { 7 } q ^ { 11 }$ 
B)  $- 2 x ^ { 7 } q ^ { 9 }$ 
C)  $- 2 x ^ { 9 } q ^ { 10 }$ 
D)  $- 2 x ^ { 8 } q ^ { 9 }$ 
A)  $- 2 x ^ { 7 } q ^ { 11 }$ 
B)  $- 2 x ^ { 7 } q ^ { 9 }$ 
C)  $- 2 x ^ { 9 } q ^ { 10 }$ 
D)  $- 2 x ^ { 8 } q ^ { 9 }$

Question 20

Perform the division of the polynomials by monomials. $\frac { 20 p ^ { 5 } + 45 p ^ { 12 } + 30 p ^ { 15 } } { 5 p ^ { 3 } }$

Accepted Answer

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

Find the indicated product by using the shortcut pattern for multiplying binomials. ( x + 3)( x + 9)

Divide the monomials. $\frac { 6 p w } { - p w }$

Find the indicated product by applying the distributive property. ( x $-$ 9)( y $-$ 8)

Perform the division and find the quotient. $\left( 10 y ^ { 2 } + 49 y + 49 \right) \div ( 2 y + 7 )$

Add the polynomials. $2 x + 9 \text { and } 11 x + 5$

A square piece of cardboard is y = 15 inches long on each side. From each corner a square piece x inches on a side is cut out as shown. The flaps are then turned up to form an open box. Find a polynomial that represents the volume of the box.

Multiply the following. $\left( - 6 a ^ { 3 } y ^ { 4 } \right) ( 12 a y )$ Enter your answer as $k a ^ { p } y ^ { q }$ where k , p , q are numbers and a , y are variables.

Find the product. $\left( x ^ { 4 n } \right) \left( x ^ { 5 n } \right)$ Assume that the variables in the exponents represent positive integers; for example, $\left( x ^ { 2 n } \right) \left( x ^ { 4 n } \right) = x ^ { 2 n + 4 n } = x ^ { 6 n }$ .

Perform the division. $\frac { 8 n ^ { 3 } - 27 } { 2 n - 3 }$

Perform the division. $\left( 6 y ^ { 3 } - y ^ { 2 } - 16 y - 12 \right) \div ( y - 2 )$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 9 y ^ { - 3 } \right) \left( 10 y ^ { 8 } \right)$

Write the following number in scientific notation. 649

Find $( x + 5 ) ^ { 3 }$ . Don t forget that $( x + 5 ) ^ { 3 }$ means ( x + 5)( x + 5)( x + 5).

Perform the indicated operations and simplify. $( 5 x ) ^ { 3 } \left( 4 x ^ { 3 } \right)$

Simplify the following algebraic expression and express your answer using positive exponents only. $b ^ { - 1 } b ^ { - 4 }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( a ^ { - 5 } b ^ { - 2 } \right) ^ { 4 }$

Perform the division and find the quotient. Answer does not include the remainder. $\frac { 5 y ^ { 3 } + 21 y ^ { 2 } - 17 y + 8 } { y + 5 }$

Remove the parentheses by multiplying and then simplify by combining similar terms. $6 ( x + 8 y ) + 3 ( 3 x + 7 y )$

Divide the monomials. $\frac { - 10 x ^ { 9 } q ^ { 11 } } { 5 x ^ { 2 } q ^ { 2 } }$

Perform the division of the polynomials by monomials. $\frac { 20 p ^ { 5 } + 45 p ^ { 12 } + 30 p ^ { 15 } } { 5 p ^ { 3 } }$

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 product by using the shortcut pattern for multiplying binomials. ( x + 3)( x + 9)

Divide the monomials. 6pw−pw\frac { 6 p w } { - p w }−pw6pw​

Find the indicated product by applying the distributive property. ( x −-− 9)( y −-− 8)

Perform the division and find the quotient. (10y2+49y+49)÷(2y+7)\left( 10 y ^ { 2 } + 49 y + 49 \right) \div ( 2 y + 7 )(10y2+49y+49)÷(2y+7)

Add the polynomials. 2x+9 and 11x+52 x + 9 \text { and } 11 x + 52x+9 and 11x+5

A square piece of cardboard is y = 15 inches long on each side. From each corner a square piece x inches on a side is cut out as shown. The flaps are then turned up to form an open box. Find a polynomial that represents the volume of the box.

Multiply the following. (−6a3y4)(12ay)\left( - 6 a ^ { 3 } y ^ { 4 } \right) ( 12 a y )(−6a3y4)(12ay) Enter your answer as kapyqk a ^ { p } y ^ { q }kapyq where k , p , q are numbers and a , y are variables.

Perform the division. 8n3−272n−3\frac { 8 n ^ { 3 } - 27 } { 2 n - 3 }2n−38n3−27​

Perform the division. (6y3−y2−16y−12)÷(y−2)\left( 6 y ^ { 3 } - y ^ { 2 } - 16 y - 12 \right) \div ( y - 2 )(6y3−y2−16y−12)÷(y−2)

Simplify the following algebraic expression and express your answer using positive exponents only. (9y−3)(10y8)\left( 9 y ^ { - 3 } \right) \left( 10 y ^ { 8 } \right)(9y−3)(10y8)

Write the following number in scientific notation. 649

Find (x+5)3( x + 5 ) ^ { 3 }(x+5)3 . Don t forget that (x+5)3( x + 5 ) ^ { 3 }(x+5)3 means ( x + 5)( x + 5)( x + 5).

Perform the indicated operations and simplify. (5x)3(4x3)( 5 x ) ^ { 3 } \left( 4 x ^ { 3 } \right)(5x)3(4x3)

Simplify the following algebraic expression and express your answer using positive exponents only. b−1b−4b ^ { - 1 } b ^ { - 4 }b−1b−4

Simplify the following algebraic expression and express your answer using positive exponents only. (a−5b−2)4\left( a ^ { - 5 } b ^ { - 2 } \right) ^ { 4 }(a−5b−2)4

Perform the division and find the quotient. Answer does not include the remainder. 5y3+21y2−17y+8y+5\frac { 5 y ^ { 3 } + 21 y ^ { 2 } - 17 y + 8 } { y + 5 }y+55y3+21y2−17y+8​

Remove the parentheses by multiplying and then simplify by combining similar terms. 6(x+8y)+3(3x+7y)6 ( x + 8 y ) + 3 ( 3 x + 7 y )6(x+8y)+3(3x+7y)

Divide the monomials. −10x9q115x2q2\frac { - 10 x ^ { 9 } q ^ { 11 } } { 5 x ^ { 2 } q ^ { 2 } }5x2q2−10x9q11​

Perform the division of the polynomials by monomials. 20p5+45p12+30p155p3\frac { 20 p ^ { 5 } + 45 p ^ { 12 } + 30 p ^ { 15 } } { 5 p ^ { 3 } }5p320p5+45p12+30p15​

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

Divide the monomials. $\frac { 6 p w } { - p w }$

Find the indicated product by applying the distributive property. ( x $-$ 9)( y $-$ 8)

Perform the division and find the quotient. $\left( 10 y ^ { 2 } + 49 y + 49 \right) \div ( 2 y + 7 )$

Add the polynomials. $2 x + 9 \text { and } 11 x + 5$

Multiply the following. $\left( - 6 a ^ { 3 } y ^ { 4 } \right) ( 12 a y )$ Enter your answer as $k a ^ { p } y ^ { q }$ where k , p , q are numbers and a , y are variables.

Perform the division. $\frac { 8 n ^ { 3 } - 27 } { 2 n - 3 }$

Perform the division. $\left( 6 y ^ { 3 } - y ^ { 2 } - 16 y - 12 \right) \div ( y - 2 )$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 9 y ^ { - 3 } \right) \left( 10 y ^ { 8 } \right)$

Find $( x + 5 ) ^ { 3 }$ . Don t forget that $( x + 5 ) ^ { 3 }$ means ( x + 5)( x + 5)( x + 5).

Perform the indicated operations and simplify. $( 5 x ) ^ { 3 } \left( 4 x ^ { 3 } \right)$

Simplify the following algebraic expression and express your answer using positive exponents only. $b ^ { - 1 } b ^ { - 4 }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( a ^ { - 5 } b ^ { - 2 } \right) ^ { 4 }$

Perform the division and find the quotient. Answer does not include the remainder. $\frac { 5 y ^ { 3 } + 21 y ^ { 2 } - 17 y + 8 } { y + 5 }$

Remove the parentheses by multiplying and then simplify by combining similar terms. $6 ( x + 8 y ) + 3 ( 3 x + 7 y )$

Divide the monomials. $\frac { - 10 x ^ { 9 } q ^ { 11 } } { 5 x ^ { 2 } q ^ { 2 } }$

Perform the division of the polynomials by monomials. $\frac { 20 p ^ { 5 } + 45 p ^ { 12 } + 30 p ^ { 15 } } { 5 p ^ { 3 } }$