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Finding the Greatest Common Factor
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The Intercepts of a Parabola
Absolute Value Function
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Factoring the Difference of Two Squares
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Factoring Out the Opposite of the GCF
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Properties of Exponents
Scientific Notation
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Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
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Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Slopes
Graphing Lines in the Coordinate Plane
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Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
 
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Finding the Greatest Common Factor (GFC)

After studying this lesson, you will be able to:

  • Factor out GCFs.

Steps of Factoring:

1. Factor out the GCF

2. Look at the number of terms:

  • 2 Terms: Look for the Difference of 2 Squares
  • 3 Terms: Factor the Trinomial
  • 4 Terms: Factor by Grouping

3. Factor Completely

4. Check by Multiplying

This lesson will concentrate on the first step of factoring: Factoring out the GCF.

 

Example 1

Factor 10y 2 + 15y

We look for the GCF...it will be 5y

Here's how we factor: write the GCF 5y and then put parentheses: 5y

Factoring is the same as dividing, so we divide each term by 5y and we put the result in the parentheses.

10y 2 divided by 5y is 2y and 15y divided by 5y is 3: 5y ( 2y + 3 ) this is the answer

We can check the answer by multiplying 5y ( 2y + 3)

Distributing we will get 10y 2 + 15y (which matches the original problem)

 

Example 2

Factor 21ab 2 - 33 a 2 bc

We look for the GCF......it will be 3ab

Here's how we factor: write the GCF 3ab and then put parentheses: 3ab

Factoring is the same as dividing, so we divide each term by 3ab and we put the result in the parentheses.

21ab 2 divided by 3ab is 7b and - 33 a 2 bc divided by 3ab is -11ac: 3ab ( 7b - 11ac ) this is the answer

We can check the answer by multiplying : 3ab ( 7b - 11ac )

Distributing we will get 21ab 2 - 33 a 2 bc (which matches the original problem)

 

Example 3

Factor 6x 3 y 2 + 14x 2 y + 2x 2

We look for the GCF......it will be 2x 2

Here's how we factor: write the GCF 2x 2 and then put parentheses: 2x 2

Factoring is the same as dividing, so we divide each term by 2x 2 and we put the result in the parentheses.

6x 3 y 2 divided by 2x 2 is 3xy 2 and 14x 2 y divided by 2x 2 is 7y and 2x 2 divided by 2x 2 is 1

2x 2(3xy 2 + 7 y + 1) this is the answer

We can check the answer by multiplying : 2x 2(3xy 2 + 7 y + 1)

Distributing we will get 6x 3 y 2 + 14x 2 y + 2x 2 (which matches the original problem)

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