Question 1

Factor this trinomial completely. $20 x ^ { 2 } - 33 x y + 10 y ^ { 2 }$

Accepted Answer

A)  (4 x $-$ 5 y )(5 x + 2 y ) 
B)  (4 x + 5 y )(5 x $-$ 2 y ) 
C)  (4 x $-$ 5 y )(5 x $-$ 2 y ) 
D)  (4 x + 5 y )(5 x + 2 y ) 
E)  not factorable 
A)  (4 x $-$ 5 y )(5 x + 2 y ) 
B)  (4 x + 5 y )(5 x $-$ 2 y ) 
C)  (4 x $-$ 5 y )(5 x $-$ 2 y ) 
D)  (4 x + 5 y )(5 x + 2 y ) 
E)  not factorable

Question 2

Factor the polynomial completely. $16 a ^ { 4 } + 25 a ^ { 2 }$

Accepted Answer

The answer of Factor the polynomial completely. \(16 a ^...

Question 3

Factor the following polynomial completely. $8 u ^ { 2 } + 42 u + 40$

Accepted Answer

The answer of Factor the following polynomial completely. \(8 u...

Question 4

Solve the equation. $- x ^ { 2 } - 3 x + 40 = 0$

Accepted Answer

A)  {3, -40} 
B)  {5, 8} 
C)  {-5, 8} 
D)  {-5, -8} 
E)  {5, -8} 
A)  {3, -40} 
B)  {5, 8} 
C)  {-5, 8} 
D)  {-5, -8} 
E)  {5, -8}

Question 5

Factor the following polynomial completely. $5 p ^ { 4 } - 405$

Accepted Answer

The answer of Factor the following polynomial completely. \(5 p...

Question 6

Solve the equation. $4 t ^ { 2 } + 27 t - 7 = 0$

Accepted Answer

The answer of Solve the equation. \(4 t ^ {...

Question 7

Solve the equation. $y ^ { 2 } - 5 y = 0$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(y ^ { 2...

Question 8

The perimeter of a rectangle is 34 centimeters and the area is 66 square centimeters. Find the length and width of the rectangle. Please enter your answer as two numbers without the units, separated by a comma.

Accepted Answer

The answer of The perimeter of a rectangle is 34...

Question 9

Factor the polynomial completely. $9 z ^ { 4 } d ^ { 9 } + 4 z ^ { 12 } d ^ { 5 }$

Accepted Answer

A)  $z ^ { 4 } d ^ { 5 } ( 9 d + 4 z )$ 
B)  $36 z ^ { 4 } d ^ { 5 } \left( 9 d ^ { 4 } + 4 z ^ { 8 } \right)$ 
C)  $z ^ { 4 } d ^ { 5 } \left( 9 d ^ { 4 } - 4 z ^ { 12 } \right)$ 
D)  $z ^ { 4 } d ^ { 5 } \left( 9 d ^ { 4 } + 4 z ^ { 8 } \right)$ 
A)  $z ^ { 4 } d ^ { 5 } ( 9 d + 4 z )$ 
B)  $36 z ^ { 4 } d ^ { 5 } \left( 9 d ^ { 4 } + 4 z ^ { 8 } \right)$ 
C)  $z ^ { 4 } d ^ { 5 } \left( 9 d ^ { 4 } - 4 z ^ { 12 } \right)$ 
D)  $z ^ { 4 } d ^ { 5 } \left( 9 d ^ { 4 } + 4 z ^ { 8 } \right)$

Question 10

Factor the following trinomial assuming that all variables appearing as exponents represent positive integers. $x ^ { 2 a } + 10 x ^ { a } + 24$

Accepted Answer

A)  $\left( x ^ { a } + 6 \right) \left( x ^ { a } + 4 \right)$ 
B)  $\left( x ^ { a } - 6 \right) \left( x ^ { a } + 4 \right)$ 
C)  $( x + 6 ) ( x + 4 )$ 
D)  $\left( x ^ { a } + 6 \right) \left( x ^ { a } - 4 \right)$ 
E)  $\left( x ^ { a } - 6 \right) \left( x ^ { a } - 4 \right)$ 
A)  $\left( x ^ { a } + 6 \right) \left( x ^ { a } + 4 \right)$ 
B)  $\left( x ^ { a } - 6 \right) \left( x ^ { a } + 4 \right)$ 
C)  $( x + 6 ) ( x + 4 )$ 
D)  $\left( x ^ { a } + 6 \right) \left( x ^ { a } - 4 \right)$ 
E)  $\left( x ^ { a } - 6 \right) \left( x ^ { a } - 4 \right)$

Question 11

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 36 y ^ { 2 }$

Accepted Answer

A)  ( x $-$ 6 y ) ( x $-$ 36 y ) 
B)  ( x $-$ 36 y ) ( x + 36 y ) 
C)  ( x $-$ 6 y ) ( x + 6 y ) 
D)  ( x + 6 y ) ( x + 36 y ) 
E)  none of these 
A)  ( x $-$ 6 y ) ( x $-$ 36 y ) 
B)  ( x $-$ 36 y ) ( x + 36 y ) 
C)  ( x $-$ 6 y ) ( x + 6 y ) 
D)  ( x + 6 y ) ( x + 36 y ) 
E)  none of these

Question 12

Solve the equation. $n ^ { 3 } = 4 n$ Please enter your answer as three numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(n ^ { 3...

Question 13

Factor the following trinomial completely. $x ^ { 2 } + 4 x y - 12 y ^ { 2 }$

Accepted Answer

A)  ( x + 2 y )( x + 6 y ) 
B)  ( x + 2 y )( x $-$ 6 y ) 
C)  ( x $-$ 2 y )( x $-$ 6 y ) 
D)  x ( x + 4 y ) $-$ 12 y 
E)  ( x $-$ 2 y )( x + 6 y ) 
A)  ( x + 2 y )( x + 6 y ) 
B)  ( x + 2 y )( x $-$ 6 y ) 
C)  ( x $-$ 2 y )( x $-$ 6 y ) 
D)  x ( x + 4 y ) $-$ 12 y 
E)  ( x $-$ 2 y )( x + 6 y )

Question 14

Given $( x + a ) ( x + b )$ , the coefficient of the middle term is the product of a and b .

Accepted Answer

A) True 
 B)False

Question 15

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 9$

Accepted Answer

The answer of Use the difference of squares pattern to...

Question 16

Factor the following trinomial completely. $x ^ { 2 } + 5 x - 24$

Accepted Answer

A)  x ( x + 5) $-$ 24 
B)  ( x + 3)( x + 8) 
C)  ( x $-$ 3)( x + 8) 
D)  ( x $-$ 3)( x $-$ 8) 
E)  ( x + 3)( x $-$ 8) 
A)  x ( x + 5) $-$ 24 
B)  ( x + 3)( x + 8) 
C)  ( x $-$ 3)( x + 8) 
D)  ( x $-$ 3)( x $-$ 8) 
E)  ( x + 3)( x $-$ 8)

Question 17

Factor the following perfect square trinomial. $64 z ^ { 2 } + 16 z + 1$

Accepted Answer

A)  $( z - 8 ) ^ { 2 }$ 
B)  $( 8 z + 16 ) ^ { 2 }$ 
C)  $( 8 z + 1 ) ^ { 2 }$ 
D)  none of these 
A)  $( z - 8 ) ^ { 2 }$ 
B)  $( 8 z + 16 ) ^ { 2 }$ 
C)  $( 8 z + 1 ) ^ { 2 }$ 
D)  none of these

Question 18

Use the process of factoring by grouping to factor the polynomial. $- 8 z ^ { 2 } + z + 32 z - 4$

Accepted Answer

A)  $( 8 z + 32 ) ( z - 1 )$ 
B)  $( - 8 z + 1 ) ( z - 4 )$ 
C)  $( - 8 z + 32 ) ( z - 4 )$ 
D)  $( - 8 z - 1 ) ( z + 4 )$ 
A)  $( 8 z + 32 ) ( z - 1 )$ 
B)  $( - 8 z + 1 ) ( z - 4 )$ 
C)  $( - 8 z + 32 ) ( z - 4 )$ 
D)  $( - 8 z - 1 ) ( z + 4 )$

Question 19

Suppose that one leg of a right triangle is 14 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the lengths of all three sides of the right triangle. Please enter your answer as three numbers without the units, separated by a comma.

Accepted Answer

The answer of Suppose that one leg of a right...

Question 20

The length of a rectangular sheet of paper is 1centimeter more than twice its width and the area of the rectangle is 105 square centimeters. Find the length of the rectangle. __________ centimeters

Accepted Answer

The answer of The length of a rectangular sheet of...

Factor this trinomial completely. $20 x ^ { 2 } - 33 x y + 10 y ^ { 2 }$

Factor the polynomial completely. $16 a ^ { 4 } + 25 a ^ { 2 }$

Factor the following polynomial completely. $8 u ^ { 2 } + 42 u + 40$

Solve the equation. $- x ^ { 2 } - 3 x + 40 = 0$

Factor the following polynomial completely. $5 p ^ { 4 } - 405$

Solve the equation. $4 t ^ { 2 } + 27 t - 7 = 0$

Solve the equation. $y ^ { 2 } - 5 y = 0$ Please enter your answer as two numbers, separated by a comma.

The perimeter of a rectangle is 34 centimeters and the area is 66 square centimeters. Find the length and width of the rectangle. Please enter your answer as two numbers without the units, separated by a comma.

Factor the polynomial completely. $9 z ^ { 4 } d ^ { 9 } + 4 z ^ { 12 } d ^ { 5 }$

Factor the following trinomial assuming that all variables appearing as exponents represent positive integers. $x ^ { 2 a } + 10 x ^ { a } + 24$

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 36 y ^ { 2 }$

Solve the equation. $n ^ { 3 } = 4 n$ Please enter your answer as three numbers, separated by a comma.

Factor the following trinomial completely. $x ^ { 2 } + 4 x y - 12 y ^ { 2 }$

Given $( x + a ) ( x + b )$ , the coefficient of the middle term is the product of a and b .

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 9$

Factor the following trinomial completely. $x ^ { 2 } + 5 x - 24$

Factor the following perfect square trinomial. $64 z ^ { 2 } + 16 z + 1$

Use the process of factoring by grouping to factor the polynomial. $- 8 z ^ { 2 } + z + 32 z - 4$

Suppose that one leg of a right triangle is 14 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the lengths of all three sides of the right triangle. Please enter your answer as three numbers without the units, separated by a comma.

The length of a rectangular sheet of paper is 1centimeter more than twice its width and the area of the rectangle is 105 square centimeters. Find the length of the rectangle. __________ centimeters

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

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 7: Factoring, Solving Equations and Problem Solving

Factor this trinomial completely. 20x2−33xy+10y220 x ^ { 2 } - 33 x y + 10 y ^ { 2 }20x2−33xy+10y2

Factor the polynomial completely. 16a4+25a216 a ^ { 4 } + 25 a ^ { 2 }16a4+25a2

Factor the following polynomial completely. 8u2+42u+408 u ^ { 2 } + 42 u + 408u2+42u+40

Solve the equation. −x2−3x+40=0- x ^ { 2 } - 3 x + 40 = 0−x2−3x+40=0

Factor the following polynomial completely. 5p4−4055 p ^ { 4 } - 4055p4−405

Solve the equation. 4t2+27t−7=04 t ^ { 2 } + 27 t - 7 = 04t2+27t−7=0

Solve the equation. y2−5y=0y ^ { 2 } - 5 y = 0y2−5y=0 Please enter your answer as two numbers, separated by a comma.

The perimeter of a rectangle is 34 centimeters and the area is 66 square centimeters. Find the length and width of the rectangle. Please enter your answer as two numbers without the units, separated by a comma.

Factor the polynomial completely. 9z4d9+4z12d59 z ^ { 4 } d ^ { 9 } + 4 z ^ { 12 } d ^ { 5 }9z4d9+4z12d5

Factor the following trinomial assuming that all variables appearing as exponents represent positive integers. x2a+10xa+24x ^ { 2 a } + 10 x ^ { a } + 24x2a+10xa+24

Use the difference of squares pattern to factor the polynomial. x2−36y2x ^ { 2 } - 36 y ^ { 2 }x2−36y2

Solve the equation. n3=4nn ^ { 3 } = 4 nn3=4n Please enter your answer as three numbers, separated by a comma.

Factor the following trinomial completely. x2+4xy−12y2x ^ { 2 } + 4 x y - 12 y ^ { 2 }x2+4xy−12y2

Given (x+a)(x+b)( x + a ) ( x + b )(x+a)(x+b) , the coefficient of the middle term is the product of a and b .

Use the difference of squares pattern to factor the polynomial. x2−9x ^ { 2 } - 9x2−9

Factor the following trinomial completely. x2+5x−24x ^ { 2 } + 5 x - 24x2+5x−24

Factor the following perfect square trinomial. 64z2+16z+164 z ^ { 2 } + 16 z + 164z2+16z+1

Use the process of factoring by grouping to factor the polynomial. −8z2+z+32z−4- 8 z ^ { 2 } + z + 32 z - 4−8z2+z+32z−4

Suppose that one leg of a right triangle is 14 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the lengths of all three sides of the right triangle. Please enter your answer as three numbers without the units, separated by a comma.

The length of a rectangular sheet of paper is 1centimeter more than twice its width and the area of the rectangle is 105 square centimeters. Find the length of the rectangle. __________ centimeters

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

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

Factor this trinomial completely. $20 x ^ { 2 } - 33 x y + 10 y ^ { 2 }$

Factor the polynomial completely. $16 a ^ { 4 } + 25 a ^ { 2 }$

Factor the following polynomial completely. $8 u ^ { 2 } + 42 u + 40$

Solve the equation. $- x ^ { 2 } - 3 x + 40 = 0$

Factor the following polynomial completely. $5 p ^ { 4 } - 405$

Solve the equation. $4 t ^ { 2 } + 27 t - 7 = 0$

Solve the equation. $y ^ { 2 } - 5 y = 0$ Please enter your answer as two numbers, separated by a comma.

Factor the polynomial completely. $9 z ^ { 4 } d ^ { 9 } + 4 z ^ { 12 } d ^ { 5 }$

Factor the following trinomial assuming that all variables appearing as exponents represent positive integers. $x ^ { 2 a } + 10 x ^ { a } + 24$

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 36 y ^ { 2 }$

Solve the equation. $n ^ { 3 } = 4 n$ Please enter your answer as three numbers, separated by a comma.

Factor the following trinomial completely. $x ^ { 2 } + 4 x y - 12 y ^ { 2 }$

Given $( x + a ) ( x + b )$ , the coefficient of the middle term is the product of a and b .

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 9$

Factor the following trinomial completely. $x ^ { 2 } + 5 x - 24$

Factor the following perfect square trinomial. $64 z ^ { 2 } + 16 z + 1$

Use the process of factoring by grouping to factor the polynomial. $- 8 z ^ { 2 } + z + 32 z - 4$