Question 1

Perform the division of the polynomials by monomials. $\frac { - 110 y ^ { 5 } - 20 y ^ { 10 } + 50 y ^ { 20 } } { 10 y ^ { 3 } }$

Accepted Answer

A)  $- 11 y ^ { 2 } - 220 y ^ { 7 }$ 
B)  $- 11 y ^ { 8 } + 2 y ^ { 7 } + 5 y ^ { 7 }$ 
C)  $- 11 y ^ { 2 } - 2 y ^ { 7 } + 5 y ^ { 17 }$ 
A)  $- 11 y ^ { 2 } - 220 y ^ { 7 }$ 
B)  $- 11 y ^ { 8 } + 2 y ^ { 7 } + 5 y ^ { 7 }$ 
C)  $- 11 y ^ { 2 } - 2 y ^ { 7 } + 5 y ^ { 17 }$

Question 2

Use scientific notation and the properties of exponents to evaluate the following numerical expression. (0.008)(170)

Accepted Answer

A)  0.136 
B)  1.36 
C)  136 
D)  13.6 
A)  0.136 
B)  1.36 
C)  136 
D)  13.6

Question 3

Subtract the polynomials using a horizontal format. $- 11 p ^ { 4 } - 9 p ^ { 3 } + 2 \text { from } 3 p ^ { 4 } + 4 p ^ { 3 } + 6$

Accepted Answer

A)  $- 14 p ^ { 4 } - 13 p ^ { 3 } - 4$ 
B)  $14 p ^ { 4 } - 13 p ^ { 3 } + 4$ 
C)  $- 14 p ^ { 4 } + 13 p ^ { 3 } - 4$ 
D)  $14 p ^ { 4 } + 13 p ^ { 3 } + 4$ 
A)  $- 14 p ^ { 4 } - 13 p ^ { 3 } - 4$ 
B)  $14 p ^ { 4 } - 13 p ^ { 3 } + 4$ 
C)  $- 14 p ^ { 4 } + 13 p ^ { 3 } - 4$ 
D)  $14 p ^ { 4 } + 13 p ^ { 3 } + 4$

Question 4

Add the polynomials. $5 p ^ { 5 } + 3 p + 10 \text { and } - 9 p ^ { 5 } - 10 p + 15$

Accepted Answer

A)  $14 p ^ { 5 } + 7 p + 25$ 
B)  $- 4 p ^ { 5 } + 7 p - 25$ 
C)  $- 4 p ^ { 5 } - 7 p + 25$ 
D)  $14 p ^ { 5 } - 7 p + 25$ 
E)  $- 4 p ^ { 10 } - 7 p ^ { 2 } - 25$ 
A)  $14 p ^ { 5 } + 7 p + 25$ 
B)  $- 4 p ^ { 5 } + 7 p - 25$ 
C)  $- 4 p ^ { 5 } - 7 p + 25$ 
D)  $14 p ^ { 5 } - 7 p + 25$ 
E)  $- 4 p ^ { 10 } - 7 p ^ { 2 } - 25$

Question 5

Perform the indicated operations. $( n - 5 ) - \left( 5 n ^ { 2 } - n + 6 \right) + \left( n ^ { 2 } - 2 \right)$

Accepted Answer

The answer of Perform the indicated operations. \(( n -...

Question 6

Perform the division. $\left( 7 n ^ { 3 } - 29 n ^ { 2 } - 32 n + 10 \right) \div ( n - 5 )$

Accepted Answer

A)  $7 n ^ { 2 } - 6 n + 2$ 
B)  $6 n ^ { 2 } + 7 n + 2$ 
C)  $6 n ^ { 2 } + 7 n - 2$ 
D)  $7 n ^ { 2 } + 6 n + 2$ 
E)  $7 n ^ { 2 } + 6 n - 2$ 
A)  $7 n ^ { 2 } - 6 n + 2$ 
B)  $6 n ^ { 2 } + 7 n + 2$ 
C)  $6 n ^ { 2 } + 7 n - 2$ 
D)  $7 n ^ { 2 } + 6 n + 2$ 
E)  $7 n ^ { 2 } + 6 n - 2$

Question 7

Find the indicated product by applying the distributive property and combining similar terms. $\left( x ^ { 2 } - 5 x - 2 \right) \left( x ^ { 2 } + 9 x - 8 \right)$

Accepted Answer

A)  $x ^ { 4 } - 4 x ^ { 3 } - 53 x ^ { 2 } + 22 x + 16$ 
B)  $x ^ { 4 } + 4 x ^ { 3 } - 55 x ^ { 2 } + 22 x + 16$ 
C)  $x ^ { 4 } + 4 x ^ { 3 } - 10 x ^ { 2 } + 18 x + 8$ 
D)  $x ^ { 4 } + 4 x ^ { 3 } - 55 x ^ { 2 } + 40 x + 16$ 
E)  none of these 
A)  $x ^ { 4 } - 4 x ^ { 3 } - 53 x ^ { 2 } + 22 x + 16$ 
B)  $x ^ { 4 } + 4 x ^ { 3 } - 55 x ^ { 2 } + 22 x + 16$ 
C)  $x ^ { 4 } + 4 x ^ { 3 } - 10 x ^ { 2 } + 18 x + 8$ 
D)  $x ^ { 4 } + 4 x ^ { 3 } - 55 x ^ { 2 } + 40 x + 16$ 
E)  none of these

Question 8

Find the indicated product by applying the distributive property. ( x + 3)( y + 6)

Accepted Answer

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

Question 9

Evaluate the following numerical expression. $4 ^ { - 3 }$

Accepted Answer

The answer of Evaluate the following numerical expression. \(4 ^...

Question 10

Represent the area of the shaded region in the following figure. The length of a radius of the smaller circle is x , and the length of a radius of the larger circle is 8 x . Please enter pi to write the symbol $$\pi$$ .

Accepted Answer

The answer of Represent the area of the shaded region...

Question 11

Subtract the polynomials using a horizontal format. $2 x ^ { 5 } - 3 x ^ { 4 } + 5 \text { from } 7 x ^ { 5 } + 4 x ^ { 4 } + 7$

Accepted Answer

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

Question 12

Perform the division of the polynomials by monomials. $\frac { - 20 z ^ { 6 } + 36 z ^ { 12 } - 28 z ^ { 13 } } { - 4 z ^ { 2 } }$

Accepted Answer

A)  $5 z ^ { 4 } - 9 z ^ { 10 } + 7 z ^ { 11 }$ 
B)  $5 z ^ { 4 } - 9 z ^ { 11 } + 7 z ^ { 12 }$ 
C)  $5 z ^ { 5 } - 9 z ^ { 10 } + 7 z ^ { 12 }$ 
A)  $5 z ^ { 4 } - 9 z ^ { 10 } + 7 z ^ { 11 }$ 
B)  $5 z ^ { 4 } - 9 z ^ { 11 } + 7 z ^ { 12 }$ 
C)  $5 z ^ { 5 } - 9 z ^ { 10 } + 7 z ^ { 12 }$

Question 13

Subtract the polynomials using a horizontal format. $8 x ^ { 4 } - 10 x ^ { 2 } + 2 \text { from } 10 x ^ { 4 } + 4 x ^ { 2 } + 9$

Accepted Answer

A)  $- 2 x ^ { 4 } - 14 x ^ { 2 } - 7$ 
B)  $18 x ^ { 4 } + 14 x ^ { 2 } + 7$ 
C)  $2 x ^ { 4 } + 14 x ^ { 2 } + 7$ 
D)  $- 2 x ^ { 4 } + 14 x ^ { 2 } + 7$ 
E)  $2 x ^ { 4 } + 14 x ^ { 2 } - 7$ 
A)  $- 2 x ^ { 4 } - 14 x ^ { 2 } - 7$ 
B)  $18 x ^ { 4 } + 14 x ^ { 2 } + 7$ 
C)  $2 x ^ { 4 } + 14 x ^ { 2 } + 7$ 
D)  $- 2 x ^ { 4 } + 14 x ^ { 2 } + 7$ 
E)  $2 x ^ { 4 } + 14 x ^ { 2 } - 7$

Question 14

Determine the degree of the polynomial. $2 p ^ { 3 } + 3 p ^ { 2 } + 12 p$

Accepted Answer

The answer of Determine the degree of the polynomial. \(2...

Question 15

Find the indicated product by applying the distributive property and combining similar terms. $( x + 8 ) \left( x ^ { 2 } + 4 x + 9 \right)$

Accepted Answer

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

Question 16

The dividing process stops when the degree of the divisor is less than the degree of the remainder.

Accepted Answer

A) True 
 B)False

Question 17

Perform the division of the polynomials by monomials. $\frac { 108 p ^ { 12 } d ^ { 6 } - 72 p ^ { 10 } d ^ { 11 } - 81 p ^ { 16 } d ^ { 20 } } { - 9 p ^ { 2 } d ^ { 3 } }$

Accepted Answer

A)  $- 12 p ^ { 10 } d ^ { 3 } + 8 p ^ { 8 } d ^ { 8 } + 9 p ^ { 14 } d ^ { 17 }$ 
B)  $12 p ^ { 10 } d ^ { 3 } + 8 p ^ { 8 } d ^ { 8 } + 9 p ^ { 14 } d ^ { 17 }$ 
C)  $- 12 p ^ { 10 } d ^ { 3 } + 8 p ^ { 8 } d ^ { 18 } + 9 p ^ { 22 } d ^ { 31 }$ 
D)  $- 12 p ^ { 10 } d ^ { 3 } + 17 p ^ { 22 } d ^ { 25 }$ 
E)  $- 20 p ^ { 10 } d ^ { 3 } + 8 p ^ { 8 } d ^ { 8 } + 9 p ^ { 14 } d ^ { 17 }$ 
A)  $- 12 p ^ { 10 } d ^ { 3 } + 8 p ^ { 8 } d ^ { 8 } + 9 p ^ { 14 } d ^ { 17 }$ 
B)  $12 p ^ { 10 } d ^ { 3 } + 8 p ^ { 8 } d ^ { 8 } + 9 p ^ { 14 } d ^ { 17 }$ 
C)  $- 12 p ^ { 10 } d ^ { 3 } + 8 p ^ { 8 } d ^ { 18 } + 9 p ^ { 22 } d ^ { 31 }$ 
D)  $- 12 p ^ { 10 } d ^ { 3 } + 17 p ^ { 22 } d ^ { 25 }$ 
E)  $- 20 p ^ { 10 } d ^ { 3 } + 8 p ^ { 8 } d ^ { 8 } + 9 p ^ { 14 } d ^ { 17 }$

Question 18

Multiply the following. $\left( 0.2 y ^ { 2 } \right) \left( 0.7 y ^ { 3 } \right)$

Accepted Answer

A)  $1.4 y ^ { 4 }$ 
B)  $0.14 y ^ { 5 }$ 
C)  $0.014 y ^ { 5 }$ 
D)  $0.14 y ^ { 4 }$ 
A)  $1.4 y ^ { 4 }$ 
B)  $0.14 y ^ { 5 }$ 
C)  $0.014 y ^ { 5 }$ 
D)  $0.14 y ^ { 4 }$

Question 19

Divide the polynomial by the monomial. $\frac { 6 z ^ { 10 } + 30 z ^ { 13 } } { 3 z ^ { 4 } }$

Accepted Answer

A)  $3 z ^ { 6 } + 27 z ^ { 9 }$ 
B)  $2 z ^ { 14 } + 10 z ^ { 9 }$ 
C)  $2 z ^ { 6 } + 10 z ^ { 9 }$ 
D)  $2 z ^ { 6 } + 60 z ^ { 9 }$ 
E)  $3 z ^ { 6 } + 27 z ^ { 13 }$ 
A)  $3 z ^ { 6 } + 27 z ^ { 9 }$ 
B)  $2 z ^ { 14 } + 10 z ^ { 9 }$ 
C)  $2 z ^ { 6 } + 10 z ^ { 9 }$ 
D)  $2 z ^ { 6 } + 60 z ^ { 9 }$ 
E)  $3 z ^ { 6 } + 27 z ^ { 13 }$

Question 20

Perform the division and find the quotient. $\left( 9 x ^ { 2 } + 27 x + 20 \right) \div ( 3 x + 4 )$

Accepted Answer

A)  3 x $-$ 5 
B)  3 x + 5 
C)  5 x + 3 
D)  3 $-$ 5 x 
E)  5 x $-$ 3 
A)  3 x $-$ 5 
B)  3 x + 5 
C)  5 x + 3 
D)  3 $-$ 5 x 
E)  5 x $-$ 3

Perform the division of the polynomials by monomials. $\frac { - 110 y ^ { 5 } - 20 y ^ { 10 } + 50 y ^ { 20 } } { 10 y ^ { 3 } }$

Use scientific notation and the properties of exponents to evaluate the following numerical expression. (0.008)(170)

Subtract the polynomials using a horizontal format. $- 11 p ^ { 4 } - 9 p ^ { 3 } + 2 \text { from } 3 p ^ { 4 } + 4 p ^ { 3 } + 6$

Add the polynomials. $5 p ^ { 5 } + 3 p + 10 \text { and } - 9 p ^ { 5 } - 10 p + 15$

Perform the indicated operations. $( n - 5 ) - \left( 5 n ^ { 2 } - n + 6 \right) + \left( n ^ { 2 } - 2 \right)$

Perform the division. $\left( 7 n ^ { 3 } - 29 n ^ { 2 } - 32 n + 10 \right) \div ( n - 5 )$

Find the indicated product by applying the distributive property and combining similar terms. $\left( x ^ { 2 } - 5 x - 2 \right) \left( x ^ { 2 } + 9 x - 8 \right)$

Find the indicated product by applying the distributive property. ( x + 3)( y + 6)

Evaluate the following numerical expression. $4 ^ { - 3 }$

Subtract the polynomials using a horizontal format. $2 x ^ { 5 } - 3 x ^ { 4 } + 5 \text { from } 7 x ^ { 5 } + 4 x ^ { 4 } + 7$

Perform the division of the polynomials by monomials. $\frac { - 20 z ^ { 6 } + 36 z ^ { 12 } - 28 z ^ { 13 } } { - 4 z ^ { 2 } }$

Subtract the polynomials using a horizontal format. $8 x ^ { 4 } - 10 x ^ { 2 } + 2 \text { from } 10 x ^ { 4 } + 4 x ^ { 2 } + 9$

Determine the degree of the polynomial. $2 p ^ { 3 } + 3 p ^ { 2 } + 12 p$

Find the indicated product by applying the distributive property and combining similar terms. $( x + 8 ) \left( x ^ { 2 } + 4 x + 9 \right)$

The dividing process stops when the degree of the divisor is less than the degree of the remainder.

Perform the division of the polynomials by monomials. $\frac { 108 p ^ { 12 } d ^ { 6 } - 72 p ^ { 10 } d ^ { 11 } - 81 p ^ { 16 } d ^ { 20 } } { - 9 p ^ { 2 } d ^ { 3 } }$

Multiply the following. $\left( 0.2 y ^ { 2 } \right) \left( 0.7 y ^ { 3 } \right)$

Divide the polynomial by the monomial. $\frac { 6 z ^ { 10 } + 30 z ^ { 13 } } { 3 z ^ { 4 } }$

Perform the division and find the quotient. $\left( 9 x ^ { 2 } + 27 x + 20 \right) \div ( 3 x + 4 )$

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 of the polynomials by monomials. −110y5−20y10+50y2010y3\frac { - 110 y ^ { 5 } - 20 y ^ { 10 } + 50 y ^ { 20 } } { 10 y ^ { 3 } }10y3−110y5−20y10+50y20​

Use scientific notation and the properties of exponents to evaluate the following numerical expression. (0.008)(170)

Subtract the polynomials using a horizontal format. −11p4−9p3+2 from 3p4+4p3+6- 11 p ^ { 4 } - 9 p ^ { 3 } + 2 \text { from } 3 p ^ { 4 } + 4 p ^ { 3 } + 6−11p4−9p3+2 from 3p4+4p3+6

Add the polynomials. 5p5+3p+10 and −9p5−10p+155 p ^ { 5 } + 3 p + 10 \text { and } - 9 p ^ { 5 } - 10 p + 155p5+3p+10 and −9p5−10p+15

Perform the indicated operations. (n−5)−(5n2−n+6)+(n2−2)( n - 5 ) - \left( 5 n ^ { 2 } - n + 6 \right) + \left( n ^ { 2 } - 2 \right)(n−5)−(5n2−n+6)+(n2−2)

Perform the division. (7n3−29n2−32n+10)÷(n−5)\left( 7 n ^ { 3 } - 29 n ^ { 2 } - 32 n + 10 \right) \div ( n - 5 )(7n3−29n2−32n+10)÷(n−5)

Find the indicated product by applying the distributive property and combining similar terms. (x2−5x−2)(x2+9x−8)\left( x ^ { 2 } - 5 x - 2 \right) \left( x ^ { 2 } + 9 x - 8 \right)(x2−5x−2)(x2+9x−8)

Find the indicated product by applying the distributive property. ( x + 3)( y + 6)

Evaluate the following numerical expression. 4−34 ^ { - 3 }4−3

Represent the area of the shaded region in the following figure. The length of a radius of the smaller circle is x , and the length of a radius of the larger circle is 8 x . Please enter pi to write the symbol π\piπ .

Subtract the polynomials using a horizontal format. 2x5−3x4+5 from 7x5+4x4+72 x ^ { 5 } - 3 x ^ { 4 } + 5 \text { from } 7 x ^ { 5 } + 4 x ^ { 4 } + 72x5−3x4+5 from 7x5+4x4+7

Perform the division of the polynomials by monomials. −20z6+36z12−28z13−4z2\frac { - 20 z ^ { 6 } + 36 z ^ { 12 } - 28 z ^ { 13 } } { - 4 z ^ { 2 } }−4z2−20z6+36z12−28z13​

Subtract the polynomials using a horizontal format. 8x4−10x2+2 from 10x4+4x2+98 x ^ { 4 } - 10 x ^ { 2 } + 2 \text { from } 10 x ^ { 4 } + 4 x ^ { 2 } + 98x4−10x2+2 from 10x4+4x2+9

Determine the degree of the polynomial. 2p3+3p2+12p2 p ^ { 3 } + 3 p ^ { 2 } + 12 p2p3+3p2+12p

Find the indicated product by applying the distributive property and combining similar terms. (x+8)(x2+4x+9)( x + 8 ) \left( x ^ { 2 } + 4 x + 9 \right)(x+8)(x2+4x+9)

The dividing process stops when the degree of the divisor is less than the degree of the remainder.

Perform the division of the polynomials by monomials. 108p12d6−72p10d11−81p16d20−9p2d3\frac { 108 p ^ { 12 } d ^ { 6 } - 72 p ^ { 10 } d ^ { 11 } - 81 p ^ { 16 } d ^ { 20 } } { - 9 p ^ { 2 } d ^ { 3 } }−9p2d3108p12d6−72p10d11−81p16d20​

Multiply the following. (0.2y2)(0.7y3)\left( 0.2 y ^ { 2 } \right) \left( 0.7 y ^ { 3 } \right)(0.2y2)(0.7y3)

Divide the polynomial by the monomial. 6z10+30z133z4\frac { 6 z ^ { 10 } + 30 z ^ { 13 } } { 3 z ^ { 4 } }3z46z10+30z13​

Perform the division and find the quotient. (9x2+27x+20)÷(3x+4)\left( 9 x ^ { 2 } + 27 x + 20 \right) \div ( 3 x + 4 )(9x2+27x+20)÷(3x+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 of the polynomials by monomials. $\frac { - 110 y ^ { 5 } - 20 y ^ { 10 } + 50 y ^ { 20 } } { 10 y ^ { 3 } }$

Subtract the polynomials using a horizontal format. $- 11 p ^ { 4 } - 9 p ^ { 3 } + 2 \text { from } 3 p ^ { 4 } + 4 p ^ { 3 } + 6$

Add the polynomials. $5 p ^ { 5 } + 3 p + 10 \text { and } - 9 p ^ { 5 } - 10 p + 15$

Perform the indicated operations. $( n - 5 ) - \left( 5 n ^ { 2 } - n + 6 \right) + \left( n ^ { 2 } - 2 \right)$

Perform the division. $\left( 7 n ^ { 3 } - 29 n ^ { 2 } - 32 n + 10 \right) \div ( n - 5 )$

Find the indicated product by applying the distributive property and combining similar terms. $\left( x ^ { 2 } - 5 x - 2 \right) \left( x ^ { 2 } + 9 x - 8 \right)$

Evaluate the following numerical expression. $4 ^ { - 3 }$

Subtract the polynomials using a horizontal format. $2 x ^ { 5 } - 3 x ^ { 4 } + 5 \text { from } 7 x ^ { 5 } + 4 x ^ { 4 } + 7$

Perform the division of the polynomials by monomials. $\frac { - 20 z ^ { 6 } + 36 z ^ { 12 } - 28 z ^ { 13 } } { - 4 z ^ { 2 } }$

Subtract the polynomials using a horizontal format. $8 x ^ { 4 } - 10 x ^ { 2 } + 2 \text { from } 10 x ^ { 4 } + 4 x ^ { 2 } + 9$

Determine the degree of the polynomial. $2 p ^ { 3 } + 3 p ^ { 2 } + 12 p$

Find the indicated product by applying the distributive property and combining similar terms. $( x + 8 ) \left( x ^ { 2 } + 4 x + 9 \right)$

Perform the division of the polynomials by monomials. $\frac { 108 p ^ { 12 } d ^ { 6 } - 72 p ^ { 10 } d ^ { 11 } - 81 p ^ { 16 } d ^ { 20 } } { - 9 p ^ { 2 } d ^ { 3 } }$

Multiply the following. $\left( 0.2 y ^ { 2 } \right) \left( 0.7 y ^ { 3 } \right)$

Divide the polynomial by the monomial. $\frac { 6 z ^ { 10 } + 30 z ^ { 13 } } { 3 z ^ { 4 } }$

Perform the division and find the quotient. $\left( 9 x ^ { 2 } + 27 x + 20 \right) \div ( 3 x + 4 )$