Running head: [INSERT TITLE HERE]

[INSERT TITLE HERE]

Student Name

Allied American University

Author Note

This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

**Directions**: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

- Find the greatest common factor. 4, 6, 12.

- Factor. 24
*x*^{3}+ 30*x*^{2}

- Factor out the GCF with a negative coefficient. –24
*m*^{2}*n*^{6}– 8*mn*^{5}– 32*n*^{4}

- Factor completely by factoring out any common factors and then factoring by grouping.

6*x*^{2 }– 5*xy* + 6*x* – 5*y*

- The GCF of 15
*y*+ 20 is 5. The GCF of 15*y*+ 21 is 3. Find the GCF of the product (15*y*+ 20)(15*y*+ 21).

- The area of a rectangle of length
*x*is given by 15*x*–*x*^{2}. Find the width of the rectangle in terms of*x*.

- Factor the trinomial completely.
*x*^{2}+ 8*x*– 9

- Factor the trinomial completely. 2
*x*^{2}+ 16*x*+ 32

- Complete the following statement. 6
*a*^{2}– 5*a*+ 1 = (3*a*– 1)(__?__)

- State whether the following is true or false.
*x*^{2}– 7*x*– 30 = (*x*+ 3)(*x*– 10)

- Factor completely.
*x*^{2}+ 11*x*+ 28

- Factor completely. 15
*x*^{2}+ 23*x*+ 4

- Factor completely. 6
*z*^{3}– 27*z*^{2}+ 12*z*

- The number of hot dogs sold at the concession stand during each hour ii
*h*after opening at a soccer tournament is given by the polynomial 2*h*^{2}– 19*h*+ 24. Write this polynomial in factored form.

- Find a positive value for
*k*for which the polynomial can be factored.*x*^{2}–*kx*+ 29

- Factor completely. 9
*x*^{2}+ 4

- Determine whether the following trinomial is a perfect square. If it is, factor the binomial.
*x*^{2}– 12*x*+ 36

- Factor completely. 25
*x*^{2}+ 40*xy*+ 16*y*^{2}

- Factor.
*s*^{2}(*t*–*u*) – 9*t*^{2}(*t*–*u*)

- State which method should be applied as the first step for factoring the polynomial. 6
*x*^{3}+ 9*x*

- State which method should be applied as the first step for factoring the polynomial. 2
*a*^{2}+ 9*a*+ 10

- Solve the quadratic equation. 5
*x*^{2}+ 17*x =*–6

- Solve the quadratic equation. 3
*x*(2*x*– 15) = –84

- The sum of an integer and its square is 30. Find the integer.

- If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm
^{2}. What were the dimensions of the original square?

- Write in simplest form.

- Write in simplest form.

- Write the expression in simplest form.

- The area of the rectangle is represented by 5
*x*^{2}+ 19*x*+ 12. What is the length?

5*x* + 4

- Multiply.

- Multiply.

- Divide.

- Divide.

- Perform the indicated operations.

- Find the area of the rectangle shown.
- Subtract. Express your answer in simplest form.

- Subtract. Express your answer in simplest form.

- Add. Express your answer in simplest form.

- Add. Express your answer in simplest form.

- Add or subtract as indicated.

- One number is 8 less than another. Let
*x*represent the larger number and use a rational expression to represent the sum of the reciprocals of the two numbers.

- Simplify.

- Simplify.

- What values for
*x*, if any, must be excluded in the following algebraic fraction?

- What values for
*x*, if any, must be excluded in the following algebraic fraction?

- Solve for
*x*. + 6 = 1

- Solve for
*x*.

- Solve for
*x*.

- One number is 3 times another. If the sum of their reciprocals is , find the two numbers.

- A 5-foot pole casts a shadow of 4 feet. How tall is a tree with a shadow of 16 feet?

Running head: [INSERT TITLE HERE]

[INSERT TITLE HERE]

Student Name

Allied American University

Author Note

This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

**Directions**: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

- Find the greatest common factor. 4, 6, 12.

- Factor. 24
*x*^{3}+ 30*x*^{2}

- Factor out the GCF with a negative coefficient. –24
*m*^{2}*n*^{6}– 8*mn*^{5}– 32*n*^{4}

- Factor completely by factoring out any common factors and then factoring by grouping.

6*x*^{2 }– 5*xy* + 6*x* – 5*y*

- The GCF of 15
*y*+ 20 is 5. The GCF of 15*y*+ 21 is 3. Find the GCF of the product (15*y*+ 20)(15*y*+ 21).

- The area of a rectangle of length
*x*is given by 15*x*–*x*^{2}. Find the width of the rectangle in terms of*x*.

- Factor the trinomial completely.
*x*^{2}+ 8*x*– 9

- Factor the trinomial completely. 2
*x*^{2}+ 16*x*+ 32

- Complete the following statement. 6
*a*^{2}– 5*a*+ 1 = (3*a*– 1)(__?__)

- State whether the following is true or false.
*x*^{2}– 7*x*– 30 = (*x*+ 3)(*x*– 10)

- Factor completely.
*x*^{2}+ 11*x*+ 28

- Factor completely. 15
*x*^{2}+ 23*x*+ 4

- Factor completely. 6
*z*^{3}– 27*z*^{2}+ 12*z*

- The number of hot dogs sold at the concession stand during each hour ii
*h*after opening at a soccer tournament is given by the polynomial 2*h*^{2}– 19*h*+ 24. Write this polynomial in factored form.

- Find a positive value for
*k*for which the polynomial can be factored.*x*^{2}–*kx*+ 29

- Factor completely. 9
*x*^{2}+ 4

- Determine whether the following trinomial is a perfect square. If it is, factor the binomial.
*x*^{2}– 12*x*+ 36

- Factor completely. 25
*x*^{2}+ 40*xy*+ 16*y*^{2}

- Factor.
*s*^{2}(*t*–*u*) – 9*t*^{2}(*t*–*u*)

- State which method should be applied as the first step for factoring the polynomial. 6
*x*^{3}+ 9*x*

- State which method should be applied as the first step for factoring the polynomial. 2
*a*^{2}+ 9*a*+ 10

- Solve the quadratic equation. 5
*x*^{2}+ 17*x =*–6

- Solve the quadratic equation. 3
*x*(2*x*– 15) = –84

- The sum of an integer and its square is 30. Find the integer.

- If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm
^{2}. What were the dimensions of the original square?

- Write in simplest form.

- Write in simplest form.

- Write the expression in simplest form.

- The area of the rectangle is represented by 5
*x*^{2}+ 19*x*+ 12. What is the length?

5*x* + 4

- Multiply.

- Multiply.

- Divide.

- Divide.

- Perform the indicated operations.

- Find the area of the rectangle shown.
- Subtract. Express your answer in simplest form.

- Subtract. Express your answer in simplest form.

- Add. Express your answer in simplest form.

- Add. Express your answer in simplest form.

- Add or subtract as indicated.

- One number is 8 less than another. Let
*x*represent the larger number and use a rational expression to represent the sum of the reciprocals of the two numbers.

- Simplify.

- Simplify.

- What values for
*x*, if any, must be excluded in the following algebraic fraction?

- What values for
*x*, if any, must be excluded in the following algebraic fraction?

- Solve for
*x*. + 6 = 1

- Solve for
*x*.

- Solve for
*x*.

- One number is 3 times another. If the sum of their reciprocals is , find the two numbers.

- A 5-foot pole casts a shadow of 4 feet. How tall is a tree with a shadow of 16 feet?

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