Question 1

Evaluate the numerical expression. $\frac { 2 ^ { 4 } } { 2 ^ { - 2 } }$

Accepted Answer

A)  $16$ 
B)  $4$ 
C)  $64$ 
D)  $\frac { 1 } { 64 }$ 
E)  $\frac { 1 } { 4 }$ 
A)  $16$ 
B)  $4$ 
C)  $64$ 
D)  $\frac { 1 } { 64 }$ 
E)  $\frac { 1 } { 4 }$ C

Question 2

Perform the division. $\left( x ^ { 2 } + 8 x - 33 \right) \div ( x - 3 )$

Accepted Answer

A)  3 x $-$ 11 
B)  x $-$ 11 
C)  3 x + 11 
D)  11 $-$ x 
E)  x + 11 
A)  3 x $-$ 11 
B)  x $-$ 11 
C)  3 x + 11 
D)  11 $-$ x 
E)  x + 11 E

Question 3

Perform the division. $\left( x ^ { 3 } - 27 x + 10 \right) \div ( x - 5 )$

Accepted Answer

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

Question 4

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 12, b = 3 and c = 7.

Accepted Answer

The answer of Find a polynomial that represents the perimeter...

Question 5

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( \frac { u ^ { - 6 } } { v ^ { - 5 } } \right) ^ { - 1 }$

Accepted Answer

A)  $\frac { u ^ { 5 } } { v ^ { 6 } }$ 
B)  $\frac { v ^ { 5 } } { u ^ { 6 } }$ 
C)  $u ^ { 6 } v ^ { 5 }$ 
D)  $\frac { u ^ { 6 } } { v ^ { 5 } }$ 
E)  $u ^ { 5 } v ^ { 6 }$ 
A)  $\frac { u ^ { 5 } } { v ^ { 6 } }$ 
B)  $\frac { v ^ { 5 } } { u ^ { 6 } }$ 
C)  $u ^ { 6 } v ^ { 5 }$ 
D)  $\frac { u ^ { 6 } } { v ^ { 5 } }$ 
E)  $u ^ { 5 } v ^ { 6 }$

Question 6

Evaluate the numerical expression. $\frac { 1 } { 6 ^ { - 3 } }$

Accepted Answer

A)  $- \frac { 1 } { 216 }$ 
B)  $18$ 
C)  $- \frac { 1 } { 18 }$ 
D)  $- 216$ 
E)  $216$ 
A)  $- \frac { 1 } { 216 }$ 
B)  $18$ 
C)  $- \frac { 1 } { 18 }$ 
D)  $- 216$ 
E)  $216$

Question 7

Perform the division. $\left( 3 x ^ { 3 } + 7 x ^ { 2 } - 21 x - 4 \right) \div ( x + 4 )$

Accepted Answer

A)  $3 x ^ { 2 } - 5 x + 1$ 
B)  $3 x ^ { 2 } + 5 x + 1$ 
C)  $5 x ^ { 2 } - 3 x + 1$ 
D)  $3 x ^ { 2 } - 5 x - 1$ 
E)  $5 x ^ { 2 } - 3 x - 1$ 
A)  $3 x ^ { 2 } - 5 x + 1$ 
B)  $3 x ^ { 2 } + 5 x + 1$ 
C)  $5 x ^ { 2 } - 3 x + 1$ 
D)  $3 x ^ { 2 } - 5 x - 1$ 
E)  $5 x ^ { 2 } - 3 x - 1$

Question 8

Multiply. $\left( 0.4 a ^ { 4 } \right) \left( 0.5 a ^ { 4 } \right)$

Accepted Answer

A)  $2 a ^ { 7 }$ 
B)  $0.2 a ^ { 8 }$ 
C)  $0.2 a ^ { 7 }$ 
D)  $0.02 a ^ { 8 }$ 
E)  $0.2 a ^ { 16 }$ 
A)  $2 a ^ { 7 }$ 
B)  $0.2 a ^ { 8 }$ 
C)  $0.2 a ^ { 7 }$ 
D)  $0.02 a ^ { 8 }$ 
E)  $0.2 a ^ { 16 }$

Question 9

Perform the division. $\left( 6 y ^ { 3 } - 5 y ^ { 2 } - 18 y + 8 \right) \div ( y - 2 )$

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Find the indicated products by using the shortcut pattern for multiplying binomials. (6 x + 9) (8 x $-$ 2)

Accepted Answer

A)  $48 x ^ { 2 } + 60 x + 18$ 
B)  $48 x ^ { 2 } + 72 x - 18$ 
C)  $48 x ^ { 2 } + 60 x - 18$ 
D)  $48 x ^ { 2 } + 60 x - 9$ 
E)  $6 x ^ { 2 } + 60 x - 18$ 
A)  $48 x ^ { 2 } + 60 x + 18$ 
B)  $48 x ^ { 2 } + 72 x - 18$ 
C)  $48 x ^ { 2 } + 60 x - 18$ 
D)  $48 x ^ { 2 } + 60 x - 9$ 
E)  $6 x ^ { 2 } + 60 x - 18$

Question 12

Perform the division. $\left( x ^ { 4 } - 81 \right) \div ( x - 3 )$

Accepted Answer

A)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27$ 
B)  $x ^ { 3 } - 12 x + 27$ 
C)  $x ^ { 2 } - 12 x - 27$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } + - 9 x + 27$ 
E)  $x ^ { 3 } - 3 - x ^ { 2 } + 9 x - 27$ 
A)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27$ 
B)  $x ^ { 3 } - 12 x + 27$ 
C)  $x ^ { 2 } - 12 x - 27$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } + - 9 x + 27$ 
E)  $x ^ { 3 } - 3 - x ^ { 2 } + 9 x - 27$

Question 13

Perform the division of the polynomials by monomials. $\frac { 8 p c - 72 p ^ { 14 } c ^ { 12 } + 16 p ^ { 17 } c ^ { 19 } } { - 8 p c }$

Accepted Answer

A)  $- 1 + 9 p ^ { 13 } c ^ { 12 } - 2 p ^ { 17 } c ^ { 18 }$ 
B)  $p c + 9 p ^ { 13 } c ^ { 11 } - 2 p ^ { 16 } c ^ { 18 }$ 
C)  $- 1 + 9 p ^ { 14 } c ^ { 13 } - 2 p ^ { 16 } c ^ { 20 }$ 
D)  $- 1 + 9 p ^ { 13 } c ^ { 11 } - 2 p ^ { 16 } c ^ { 18 }$ 
A)  $- 1 + 9 p ^ { 13 } c ^ { 12 } - 2 p ^ { 17 } c ^ { 18 }$ 
B)  $p c + 9 p ^ { 13 } c ^ { 11 } - 2 p ^ { 16 } c ^ { 18 }$ 
C)  $- 1 + 9 p ^ { 14 } c ^ { 13 } - 2 p ^ { 16 } c ^ { 20 }$ 
D)  $- 1 + 9 p ^ { 13 } c ^ { 11 } - 2 p ^ { 16 } c ^ { 18 }$

Question 14

Find a polynomial that represents the perimeter of the rectangle with the sides 6 x + 10 and x + 2.

Accepted Answer

A)  $4 x ^ { 2 } - 24$ 
B)  $14 x + 24$ 
C)  $8 x + 48$ 
D)  $120 x$ 
A)  $4 x ^ { 2 } - 24$ 
B)  $14 x + 24$ 
C)  $8 x + 48$ 
D)  $120 x$

Question 15

Perform the indicated operations. $4 z - \{ 9 z - [ 2 z - ( 8 z - 16 ) ] \}$

Accepted Answer

A)  $- 11 z + 16$ 
B)  $- 11 z - 16$ 
C)  $11 z - 16$ 
D)  $11 z + 16$ 
A)  $- 11 z + 16$ 
B)  $- 11 z - 16$ 
C)  $11 z - 16$ 
D)  $11 z + 16$

Question 16

Find the indicated product by applying the distributive property and combining similar terms. (9 x $-$ 8)(2 x $-$ 7)

Accepted Answer

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

Question 17

Perform the division of the polynomials by monomials. $\frac { - 36 p ^ { 7 } a - 90 p ^ { 7 } a ^ { 12 } + 27 p ^ { 7 } a ^ { 19 } } { - 9 p ^ { 7 } a }$

Accepted Answer

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

Question 18

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

Accepted Answer

A)  $9 x ^ { 2 } + 18 x y + 3 y ^ { 2 }$ 
B)  $9 x ^ { 2 } + 9 x y + 9 y ^ { 2 }$ 
C)  $9 x ^ { 2 } + 18 x y + 9 y ^ { 2 }$ 
D)  $9 x ^ { 2 } - 18 x y + 9 y ^ { 2 }$ 
E)  none of these 
A)  $9 x ^ { 2 } + 18 x y + 3 y ^ { 2 }$ 
B)  $9 x ^ { 2 } + 9 x y + 9 y ^ { 2 }$ 
C)  $9 x ^ { 2 } + 18 x y + 9 y ^ { 2 }$ 
D)  $9 x ^ { 2 } - 18 x y + 9 y ^ { 2 }$ 
E)  none of these

Question 19

Multiply. $\left( \frac { 2 } { 3 } x y \right) \left( \frac { 3 } { 11 } x ^ { 4 } y ^ { 2 } \right)$

Accepted Answer

The answer of Multiply. \(\left( \frac { 2 } {...

Question 20

Divide the monomials. $\frac { 6 x ^ { 11 } } { x ^ { 3 } }$

Accepted Answer

A)  $6 x ^ { 14 }$ 
B)  $6 x ^ { 8 }$ 
C)  $5 x ^ { 8 }$ 
D)  $5 x ^ { 14 }$ 
E)  $7 x ^ { 8 }$ 
A)  $6 x ^ { 14 }$ 
B)  $6 x ^ { 8 }$ 
C)  $5 x ^ { 8 }$ 
D)  $5 x ^ { 14 }$ 
E)  $7 x ^ { 8 }$

Evaluate the numerical expression. $\frac { 2 ^ { 4 } } { 2 ^ { - 2 } }$

Perform the division. $\left( x ^ { 2 } + 8 x - 33 \right) \div ( x - 3 )$

Perform the division. $\left( x ^ { 3 } - 27 x + 10 \right) \div ( x - 5 )$

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 12, b = 3 and c = 7.

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( \frac { u ^ { - 6 } } { v ^ { - 5 } } \right) ^ { - 1 }$

Evaluate the numerical expression. $\frac { 1 } { 6 ^ { - 3 } }$

Perform the division. $\left( 3 x ^ { 3 } + 7 x ^ { 2 } - 21 x - 4 \right) \div ( x + 4 )$

Multiply. $\left( 0.4 a ^ { 4 } \right) \left( 0.5 a ^ { 4 } \right)$

Perform the division. $\left( 6 y ^ { 3 } - 5 y ^ { 2 } - 18 y + 8 \right) \div ( y - 2 )$

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

Find the indicated products by using the shortcut pattern for multiplying binomials. (6 x + 9) (8 x $-$ 2)

Perform the division. $\left( x ^ { 4 } - 81 \right) \div ( x - 3 )$

Perform the division of the polynomials by monomials. $\frac { 8 p c - 72 p ^ { 14 } c ^ { 12 } + 16 p ^ { 17 } c ^ { 19 } } { - 8 p c }$

Find a polynomial that represents the perimeter of the rectangle with the sides 6 x + 10 and x + 2.

Perform the indicated operations. $4 z - \{ 9 z - [ 2 z - ( 8 z - 16 ) ] \}$

Find the indicated product by applying the distributive property and combining similar terms. (9 x $-$ 8)(2 x $-$ 7)

Perform the division of the polynomials by monomials. $\frac { - 36 p ^ { 7 } a - 90 p ^ { 7 } a ^ { 12 } + 27 p ^ { 7 } a ^ { 19 } } { - 9 p ^ { 7 } a }$

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

Multiply. $\left( \frac { 2 } { 3 } x y \right) \left( \frac { 3 } { 11 } x ^ { 4 } y ^ { 2 } \right)$

Divide the monomials. $\frac { 6 x ^ { 11 } } { x ^ { 3 } }$

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

Evaluate the numerical expression. 242−2\frac { 2 ^ { 4 } } { 2 ^ { - 2 } }2−224​

Perform the division. (x2+8x−33)÷(x−3)\left( x ^ { 2 } + 8 x - 33 \right) \div ( x - 3 )(x2+8x−33)÷(x−3)

Perform the division. (x3−27x+10)÷(x−5)\left( x ^ { 3 } - 27 x + 10 \right) \div ( x - 5 )(x3−27x+10)÷(x−5)

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 12, b = 3 and c = 7.

Simplify the following algebraic expression and express your answer using positive exponents only. (u−6v−5)−1\left( \frac { u ^ { - 6 } } { v ^ { - 5 } } \right) ^ { - 1 }(v−5u−6​)−1

Evaluate the numerical expression. 16−3\frac { 1 } { 6 ^ { - 3 } }6−31​

Perform the division. (3x3+7x2−21x−4)÷(x+4)\left( 3 x ^ { 3 } + 7 x ^ { 2 } - 21 x - 4 \right) \div ( x + 4 )(3x3+7x2−21x−4)÷(x+4)

Multiply. (0.4a4)(0.5a4)\left( 0.4 a ^ { 4 } \right) \left( 0.5 a ^ { 4 } \right)(0.4a4)(0.5a4)

Perform the division. (6y3−5y2−18y+8)÷(y−2)\left( 6 y ^ { 3 } - 5 y ^ { 2 } - 18 y + 8 \right) \div ( y - 2 )(6y3−5y2−18y+8)÷(y−2)

Subtract the polynomials using a horizontal format. 2p3−10p+2 from 10p3+2p+102 p ^ { 3 } - 10 p + 2 \text { from } 10 p ^ { 3 } + 2 p + 102p3−10p+2 from 10p3+2p+10

Find the indicated products by using the shortcut pattern for multiplying binomials. (6 x + 9) (8 x −-− 2)

Perform the division. (x4−81)÷(x−3)\left( x ^ { 4 } - 81 \right) \div ( x - 3 )(x4−81)÷(x−3)

Perform the division of the polynomials by monomials. 8pc−72p14c12+16p17c19−8pc\frac { 8 p c - 72 p ^ { 14 } c ^ { 12 } + 16 p ^ { 17 } c ^ { 19 } } { - 8 p c }−8pc8pc−72p14c12+16p17c19​

Find a polynomial that represents the perimeter of the rectangle with the sides 6 x + 10 and x + 2.

Perform the indicated operations. 4z−{9z−[2z−(8z−16)]}4 z - \{ 9 z - [ 2 z - ( 8 z - 16 ) ] \}4z−{9z−[2z−(8z−16)]}

Find the indicated product by applying the distributive property and combining similar terms. (9 x −-− 8)(2 x −-− 7)

Perform the division of the polynomials by monomials. −36p7a−90p7a12+27p7a19−9p7a\frac { - 36 p ^ { 7 } a - 90 p ^ { 7 } a ^ { 12 } + 27 p ^ { 7 } a ^ { 19 } } { - 9 p ^ { 7 } a }−9p7a−36p7a−90p7a12+27p7a19​

Multiply. (23xy)(311x4y2)\left( \frac { 2 } { 3 } x y \right) \left( \frac { 3 } { 11 } x ^ { 4 } y ^ { 2 } \right)(32​xy)(113​x4y2)

Divide the monomials. 6x11x3\frac { 6 x ^ { 11 } } { x ^ { 3 } }x36x11​

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

Evaluate the numerical expression. $\frac { 2 ^ { 4 } } { 2 ^ { - 2 } }$

Perform the division. $\left( x ^ { 2 } + 8 x - 33 \right) \div ( x - 3 )$

Perform the division. $\left( x ^ { 3 } - 27 x + 10 \right) \div ( x - 5 )$

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( \frac { u ^ { - 6 } } { v ^ { - 5 } } \right) ^ { - 1 }$

Evaluate the numerical expression. $\frac { 1 } { 6 ^ { - 3 } }$

Perform the division. $\left( 3 x ^ { 3 } + 7 x ^ { 2 } - 21 x - 4 \right) \div ( x + 4 )$

Multiply. $\left( 0.4 a ^ { 4 } \right) \left( 0.5 a ^ { 4 } \right)$

Perform the division. $\left( 6 y ^ { 3 } - 5 y ^ { 2 } - 18 y + 8 \right) \div ( y - 2 )$

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

Find the indicated products by using the shortcut pattern for multiplying binomials. (6 x + 9) (8 x $-$ 2)

Perform the division. $\left( x ^ { 4 } - 81 \right) \div ( x - 3 )$

Perform the division of the polynomials by monomials. $\frac { 8 p c - 72 p ^ { 14 } c ^ { 12 } + 16 p ^ { 17 } c ^ { 19 } } { - 8 p c }$

Perform the indicated operations. $4 z - \{ 9 z - [ 2 z - ( 8 z - 16 ) ] \}$

Find the indicated product by applying the distributive property and combining similar terms. (9 x $-$ 8)(2 x $-$ 7)

Perform the division of the polynomials by monomials. $\frac { - 36 p ^ { 7 } a - 90 p ^ { 7 } a ^ { 12 } + 27 p ^ { 7 } a ^ { 19 } } { - 9 p ^ { 7 } a }$

Multiply. $\left( \frac { 2 } { 3 } x y \right) \left( \frac { 3 } { 11 } x ^ { 4 } y ^ { 2 } \right)$

Divide the monomials. $\frac { 6 x ^ { 11 } } { x ^ { 3 } }$