# Algebra - Mixed Practice (Up to Factoring)

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## Algebra - Mixed Practice (Up to Factoring)

In this set of worksheets, we review content up to factoring of algebraic expressions.

New content includes difference of squares, perfect square binomials, and general quadratics. The last worksheet also includes problems which are solved by factoring a quadratic.

Other content reviewed includes solving word problems, finding LCM and GCF (which will be especially useful in the next unit when we start working with algebraic fractions), and manipulating polynomials.

Note that multiple step factoring problems are reserved for the last worksheet in this set.

**Worksheet 5.1**

- LCM and GCF
- Fraction manipulation
- Word problems
- Factoring difference of squares and perfect squares

**Worksheet 5.2**

- Multiplying and dividing monomials
- Simplifying algebraic expressions
- Factoring difference of squares and perfect squares
- Factoring general quadratics

**Worksheet 5.3**

- Simplifying expressions with positives and negatives
- Multiplying polynomials
- Factoring - multi-step problems

## Worksheet Sets in this Series

Worksheets for this section are below the index. Click the "Overview" link to get a more detailed view of the entire series.

**Mixed Practice Overview**- Mixed Practice #1 - Pre-Algebra
- Mixed Practice #2 - Algebraic Expressions
- Mixed Practice #3 - Linear Equations
- Mixed Practice #4 - Polynomial Manipulation
- Mixed Practice #5 - Factoring
- Mixed Practice #6 - Quadratic Equations
- Mixed Practice #7 - Rational Expressions
- Mixed Practice #8 - Systems of Equations
- Mixed Practice #9 - Radical Expressions

Lesson by Mr. Twitchell

## Handouts/Worksheets

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## Mixed Practice 5.1

- Find the LCM and GCF of 20 and 35

- Find the LCM and GCF of 36 and 54

- +715=310

- -+536=118

- 35
**·**=2581

- ÷16=1014

- 2 ÷ =13

- ÷ 3 =15

- If twice a number, plus three times that number, is decreased by 15, the result is 2.5 times the number. What is the number?

- The cost of some bananas purchased at $0.75 apiece is $3.12 less than the same number of apples purchased at $0.99 apiece. What is the total number of fruit purchased?

- Joey can read a certain number of pages in 3 hours. In 7 more hours, he can finish reading the entire 540 page novel. How many pages can he read in one hour?
*Factor the expressions below*

- 3x - 12

- 25x
^{2}- 16

- 9x
^{2}+ 12x + 4

- x
^{2}- 6x + 9

- -x
^{2}+ 25

- x
^{2}+ 4xy + 4y^{2}

- x14
^{2}-259

- x43
^{2}-x45

- x14
^{2}+ x + 1

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## Mixed Practice 5.1: Answer Key

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## Mixed Practice 5.2

- 12x
^{2}y · 3xy^{3}=

- xyz23
^{5}· 18x^{3}=

- x ·14xy =23

- 12x
^{3}y^{2}÷ 3xy =

- 15x
^{2}y^{3}÷ 10x^{2}=

- 10x
^{2}y^{5}÷ 2x^{2}y^{5}=

- 13x - 4(x - 2) + 10 =

- 2x[3x + (-2)(x - y) + 2] =
*Factor the following expressions*

- 5x
^{2}+ 10x

- 81x
^{2}- 25y^{2}

- 4x
^{2}- 4x + 1

- x49
^{2}- 1

- x49
^{2}-x + 143

- 10x
^{2}y^{3}+5xy

- x
^{2}+ 6x + 8

- x
^{2}- 14x + 48

- x
^{2}- 2x - 15

- 2x
^{2}- 9x + 9

- 2x
^{2}- 7x - 4

- 4x
^{2}- 8x + 3

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## Mixed Practice 5.2: Answer Key

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## Mixed Practice 5.3

- -3x + 2x
^{2}- 2x(-x + 4) =

- 5 + (-2x) - (-3) + 2x =

- 3x(1 - x
^{2}) - 2[3 - (-2x)] =

- 5{x - 3[-2 - (x - 1)] - 2} =

- (x - 1)(2x - 5) =

- 5(3x + 1)(3x - 1) =

- (x
^{2}+ x + 1)(x - 1) =

- (x
^{2}- 2x + 1)^{2}=

- (a + b + c)(a + b - c)

- (a - b - c)(a + b + c)
*Factor each expression completely*

- 2x
^{2}- 18

- x
^{4}- 16

- 2x
^{2}+ 6x + 4

- x
^{3}- 7x^{2}+ 12x

- x
^{4}- 13x^{2}+ 36

- x29
^{2}- 2

- x
^{4}- 16x^{2}

- x
^{5}- 3x^{4}- 28x^{3}

- a
^{2}+ 4ab + 4b^{2}- 9

- x
^{8}- 256

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## Mixed Practice 5.3: Answer Key

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