Question 1

Perform the division and find the quotient. Do not include the remainder in the answer. $\frac { 18 y ^ { 2 } + 30 y - 60 } { 3 y + 8 }$ Quotient: __________

Accepted Answer

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

Question 2

Perform the indicated operations. $( 2 x + 8 ) - ( 8 x - 4 ) + ( 11 x + 4 )$

Accepted Answer

The answer of Perform the indicated operations. \(( 2 x...

Question 3

Subtract the polynomials using a vertical format. $- 6 z - 12 \text { from } 7 z + 8$

Accepted Answer

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

Question 4

Divide the monomials. $\frac { 10 z ^ { 13 } } { 2 z ^ { 3 } }$

Accepted Answer

The answer of Divide the monomials. \(\frac { 10 z...

Question 5

Find $( 5 x - 4 ) ^ { 3 }$ . Don t forget that $( 5 x - 4 ) ^ { 3 }$ means (5 x - 4)(5 x - 4)(5 x - 4).

Accepted Answer

The answer of Find \(( 5 x - 4 )...

Question 6

A square piece of cardboard is y = 13 inches long on each side. From each corner a square piece x inches on a side is cut out as shown in Figure. The flaps are then turned up to form an open box. Find a polynomial that represents the volume of the box.

Accepted Answer

The answer of A square piece of cardboard is y...

Question 7

Perform the division. $\left( n ^ { 3 } - 21 n + 20 \right) \div ( n - 4 )$

Accepted Answer

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

Question 8

Subtract the polynomials using a horizontal format. $3 p ^ { 3 } - 10 p ^ { 2 } + 4 \text { from } 10 p ^ { 3 } + 5 p ^ { 2 } + 6$

Accepted Answer

A)  $7 p ^ { 3 } + 15 p ^ { 2 } - 2$ 
B)  $- 7 p ^ { 3 } + 15 p ^ { 2 } + 2$ 
C)  $- 7 p ^ { 3 } - 15 p ^ { 2 } - 2$ 
D)  $7 p ^ { 3 } + 15 p ^ { 2 } + 2$ 
A)  $7 p ^ { 3 } + 15 p ^ { 2 } - 2$ 
B)  $- 7 p ^ { 3 } + 15 p ^ { 2 } + 2$ 
C)  $- 7 p ^ { 3 } - 15 p ^ { 2 } - 2$ 
D)  $7 p ^ { 3 } + 15 p ^ { 2 } + 2$

Question 9

Perform the division of the polynomials by monomials. $\frac { 18 p ^ { 6 } + 54 p ^ { 11 } + 45 p ^ { 9 } } { 9 p ^ { 4 } }$

Accepted Answer

A)  $2 p ^ { 4 } + 6 p ^ { 7 } + 5 p ^ { 6 }$ 
B)  $2 p ^ { 2 } + 6 p ^ { 7 } + 5 p ^ { 5 }$ 
C)  $2 p ^ { 2 } + 6 p ^ { 10 } + 5 p ^ { 5 }$ 
A)  $2 p ^ { 4 } + 6 p ^ { 7 } + 5 p ^ { 6 }$ 
B)  $2 p ^ { 2 } + 6 p ^ { 7 } + 5 p ^ { 5 }$ 
C)  $2 p ^ { 2 } + 6 p ^ { 10 } + 5 p ^ { 5 }$

Question 10

Divide the monomials. $\frac { 12 z ^ { 11 } } { 3 z ^ { 2 } }$

Accepted Answer

A)  $4 z ^ { 9 }$ 
B)  $3 z ^ { 13 }$ 
C)  $33 z ^ { 9 }$ 
A)  $4 z ^ { 9 }$ 
B)  $3 z ^ { 13 }$ 
C)  $33 z ^ { 9 }$

Question 11

Express in simplified form the total surface area of the rectangular solid given below, where a = 8 and b = 5.

Accepted Answer

A)  $8 x ^ { 2 } + 45 x$ 
B)  $17 x ^ { 2 } + 93 x$ 
C)  $16 x ^ { 2 } + 90 x$ 
D)  $17 x ^ { 2 } + 90 x$ 
E)  $16 x ^ { 2 } + 93 x$ 
A)  $8 x ^ { 2 } + 45 x$ 
B)  $17 x ^ { 2 } + 93 x$ 
C)  $16 x ^ { 2 } + 90 x$ 
D)  $17 x ^ { 2 } + 90 x$ 
E)  $16 x ^ { 2 } + 93 x$

Question 12

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( x ^ { - 2 } v ^ { - 1 } \right) ^ { 3 }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 5 } v ^ { 4 } }$ 
B)  $\frac { 1 } { x ^ { 1 } v ^ { 2 } }$ 
C)  $\frac { 1 } { x ^ { 6 } v ^ { 3 } }$ 
A)  $\frac { 1 } { x ^ { 5 } v ^ { 4 } }$ 
B)  $\frac { 1 } { x ^ { 1 } v ^ { 2 } }$ 
C)  $\frac { 1 } { x ^ { 6 } v ^ { 3 } }$

Question 13

Multiply the following. ( $-$ 6 ab )(7 ab )

Accepted Answer

A)  $- 41 a b$ 
B)  $- 42 a ^ { 2 } b ^ { 2 }$ 
C)  $- 42 a ^ { 2 } b$ 
D)  $- 41 a b ^ { 2 }$ 
A)  $- 41 a b$ 
B)  $- 42 a ^ { 2 } b ^ { 2 }$ 
C)  $- 42 a ^ { 2 } b$ 
D)  $- 41 a b ^ { 2 }$

Question 14

Multiply. $( - 6 x y ) ( 8 x y )$

Accepted Answer

A)  $- 47 x y$ 
B)  $- 47 x ^ { 2 } y ^ { 2 }$ 
C)  $- 48 x ^ { 2 } y$ 
D)  $- 47 x y ^ { 2 }$ 
E)  $- 48 x ^ { 2 } y ^ { 2 }$ 
A)  $- 47 x y$ 
B)  $- 47 x ^ { 2 } y ^ { 2 }$ 
C)  $- 48 x ^ { 2 } y$ 
D)  $- 47 x y ^ { 2 }$ 
E)  $- 48 x ^ { 2 } y ^ { 2 }$

Question 15

Multiply the following. $\left( \frac { 4 } { 5 } x y \right) \left( \frac { 5 } { 11 } x ^ { 5 } y ^ { 2 } \right)$ Enter your answer as $a x ^ { b } y ^ { c }$ where b , c are numbers, a is a fraction and x , y are variables.

Accepted Answer

The answer of Multiply the following. \(\left( \frac { 4...

Question 16

Evaluate the numerical expression. $\frac { 2 ^ { 5 } } { 2 ^ { - 2 } }$

Accepted Answer

A)  $\frac { 1 } { 128 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  128 
D)  8 
A)  $\frac { 1 } { 128 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  128 
D)  8

Question 17

Find the indicated product by applying the distributive property. ( x + 4)( y + z + 8)

Accepted Answer

A)  xy + xz + 4 x + 4 y + 8 z + 32 
B)  xy + xz + 8 x + 4 y + 4 z + 32 
C)  xy + yz + 8 x + 4 y + 4 z + 4 
D)  xy + xz + 8 x + 4 y + 32 
E)  none of these 
A)  xy + xz + 4 x + 4 y + 8 z + 32 
B)  xy + xz + 8 x + 4 y + 4 z + 32 
C)  xy + yz + 8 x + 4 y + 4 z + 4 
D)  xy + xz + 8 x + 4 y + 32 
E)  none of these

Question 18

Evaluate the numerical expression. $4 ^ { - 6 } \cdot 4 ^ { 8 }$

Accepted Answer

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

Question 19

Subtract the polynomials using a horizontal format. $5 y + 16 \text { from } 8 y + 4$

Accepted Answer

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

Question 20

Perform the division. $\left( x ^ { 3 } + 64 \right) \div ( x + 4 )$

Accepted Answer

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

Perform the division and find the quotient. Do not include the remainder in the answer. $\frac { 18 y ^ { 2 } + 30 y - 60 } { 3 y + 8 }$ Quotient: __________

Perform the indicated operations. $( 2 x + 8 ) - ( 8 x - 4 ) + ( 11 x + 4 )$

Subtract the polynomials using a vertical format. $- 6 z - 12 \text { from } 7 z + 8$

Divide the monomials. $\frac { 10 z ^ { 13 } } { 2 z ^ { 3 } }$

Find $( 5 x - 4 ) ^ { 3 }$ . Don t forget that $( 5 x - 4 ) ^ { 3 }$ means (5 x - 4)(5 x - 4)(5 x - 4).

A square piece of cardboard is y = 13 inches long on each side. From each corner a square piece x inches on a side is cut out as shown in Figure. The flaps are then turned up to form an open box. Find a polynomial that represents the volume of the box.

Perform the division. $\left( n ^ { 3 } - 21 n + 20 \right) \div ( n - 4 )$

Subtract the polynomials using a horizontal format. $3 p ^ { 3 } - 10 p ^ { 2 } + 4 \text { from } 10 p ^ { 3 } + 5 p ^ { 2 } + 6$

Perform the division of the polynomials by monomials. $\frac { 18 p ^ { 6 } + 54 p ^ { 11 } + 45 p ^ { 9 } } { 9 p ^ { 4 } }$

Divide the monomials. $\frac { 12 z ^ { 11 } } { 3 z ^ { 2 } }$

Express in simplified form the total surface area of the rectangular solid given below, where a = 8 and b = 5.

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( x ^ { - 2 } v ^ { - 1 } \right) ^ { 3 }$

Multiply the following. ( $-$ 6 ab )(7 ab )

Multiply. $( - 6 x y ) ( 8 x y )$

Multiply the following. $\left( \frac { 4 } { 5 } x y \right) \left( \frac { 5 } { 11 } x ^ { 5 } y ^ { 2 } \right)$ Enter your answer as $a x ^ { b } y ^ { c }$ where b , c are numbers, a is a fraction and x , y are variables.

Evaluate the numerical expression. $\frac { 2 ^ { 5 } } { 2 ^ { - 2 } }$

Find the indicated product by applying the distributive property. ( x + 4)( y + z + 8)

Evaluate the numerical expression. $4 ^ { - 6 } \cdot 4 ^ { 8 }$

Subtract the polynomials using a horizontal format. $5 y + 16 \text { from } 8 y + 4$

Perform the division. $\left( x ^ { 3 } + 64 \right) \div ( x + 4 )$

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 quotient. Do not include the remainder in the answer. 18y2+30y−603y+8\frac { 18 y ^ { 2 } + 30 y - 60 } { 3 y + 8 }3y+818y2+30y−60​ Quotient: __________

Perform the indicated operations. (2x+8)−(8x−4)+(11x+4)( 2 x + 8 ) - ( 8 x - 4 ) + ( 11 x + 4 )(2x+8)−(8x−4)+(11x+4)

Subtract the polynomials using a vertical format. −6z−12 from 7z+8- 6 z - 12 \text { from } 7 z + 8−6z−12 from 7z+8

Divide the monomials. 10z132z3\frac { 10 z ^ { 13 } } { 2 z ^ { 3 } }2z310z13​

Find (5x−4)3( 5 x - 4 ) ^ { 3 }(5x−4)3 . Don t forget that (5x−4)3( 5 x - 4 ) ^ { 3 }(5x−4)3 means (5 x - 4)(5 x - 4)(5 x - 4).

A square piece of cardboard is y = 13 inches long on each side. From each corner a square piece x inches on a side is cut out as shown in Figure. The flaps are then turned up to form an open box. Find a polynomial that represents the volume of the box.

Perform the division. (n3−21n+20)÷(n−4)\left( n ^ { 3 } - 21 n + 20 \right) \div ( n - 4 )(n3−21n+20)÷(n−4)

Subtract the polynomials using a horizontal format. 3p3−10p2+4 from 10p3+5p2+63 p ^ { 3 } - 10 p ^ { 2 } + 4 \text { from } 10 p ^ { 3 } + 5 p ^ { 2 } + 63p3−10p2+4 from 10p3+5p2+6

Perform the division of the polynomials by monomials. 18p6+54p11+45p99p4\frac { 18 p ^ { 6 } + 54 p ^ { 11 } + 45 p ^ { 9 } } { 9 p ^ { 4 } }9p418p6+54p11+45p9​

Divide the monomials. 12z113z2\frac { 12 z ^ { 11 } } { 3 z ^ { 2 } }3z212z11​

Express in simplified form the total surface area of the rectangular solid given below, where a = 8 and b = 5.

Simplify the following algebraic expression and express your answer using positive exponents only. (x−2v−1)3\left( x ^ { - 2 } v ^ { - 1 } \right) ^ { 3 }(x−2v−1)3

Multiply the following. ( −-− 6 ab )(7 ab )

Multiply. (−6xy)(8xy)( - 6 x y ) ( 8 x y )(−6xy)(8xy)

Multiply the following. (45xy)(511x5y2)\left( \frac { 4 } { 5 } x y \right) \left( \frac { 5 } { 11 } x ^ { 5 } y ^ { 2 } \right)(54​xy)(115​x5y2) Enter your answer as axbyca x ^ { b } y ^ { c }axbyc where b , c are numbers, a is a fraction and x , y are variables.

Evaluate the numerical expression. 252−2\frac { 2 ^ { 5 } } { 2 ^ { - 2 } }2−225​

Find the indicated product by applying the distributive property. ( x + 4)( y + z + 8)

Evaluate the numerical expression. 4−6⋅484 ^ { - 6 } \cdot 4 ^ { 8 }4−6⋅48

Subtract the polynomials using a horizontal format. 5y+16 from 8y+45 y + 16 \text { from } 8 y + 45y+16 from 8y+4

Perform the division. (x3+64)÷(x+4)\left( x ^ { 3 } + 64 \right) \div ( x + 4 )(x3+64)÷(x+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

Perform the division and find the quotient. Do not include the remainder in the answer. $\frac { 18 y ^ { 2 } + 30 y - 60 } { 3 y + 8 }$ Quotient: __________

Perform the indicated operations. $( 2 x + 8 ) - ( 8 x - 4 ) + ( 11 x + 4 )$

Subtract the polynomials using a vertical format. $- 6 z - 12 \text { from } 7 z + 8$

Divide the monomials. $\frac { 10 z ^ { 13 } } { 2 z ^ { 3 } }$

Find $( 5 x - 4 ) ^ { 3 }$ . Don t forget that $( 5 x - 4 ) ^ { 3 }$ means (5 x - 4)(5 x - 4)(5 x - 4).

Perform the division. $\left( n ^ { 3 } - 21 n + 20 \right) \div ( n - 4 )$

Subtract the polynomials using a horizontal format. $3 p ^ { 3 } - 10 p ^ { 2 } + 4 \text { from } 10 p ^ { 3 } + 5 p ^ { 2 } + 6$

Perform the division of the polynomials by monomials. $\frac { 18 p ^ { 6 } + 54 p ^ { 11 } + 45 p ^ { 9 } } { 9 p ^ { 4 } }$

Divide the monomials. $\frac { 12 z ^ { 11 } } { 3 z ^ { 2 } }$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( x ^ { - 2 } v ^ { - 1 } \right) ^ { 3 }$

Multiply the following. ( $-$ 6 ab )(7 ab )

Multiply. $( - 6 x y ) ( 8 x y )$

Multiply the following. $\left( \frac { 4 } { 5 } x y \right) \left( \frac { 5 } { 11 } x ^ { 5 } y ^ { 2 } \right)$ Enter your answer as $a x ^ { b } y ^ { c }$ where b , c are numbers, a is a fraction and x , y are variables.

Evaluate the numerical expression. $\frac { 2 ^ { 5 } } { 2 ^ { - 2 } }$

Evaluate the numerical expression. $4 ^ { - 6 } \cdot 4 ^ { 8 }$

Subtract the polynomials using a horizontal format. $5 y + 16 \text { from } 8 y + 4$

Perform the division. $\left( x ^ { 3 } + 64 \right) \div ( x + 4 )$