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Finding the Greatest Common Factor
Factoring Trinomials
Absolute Value Function
A Summary of Factoring Polynomials
Solving Equations with One Radical Term
Adding Fractions
Subtracting Fractions
The FOIL Method
Graphing Compound Inequalities
Solving Absolute Value Inequalities
Adding and Subtracting Polynomials
Using Slope
Solving Quadratic Equations
Multiplication Properties of Exponents
Completing the Square
Solving Systems of Equations by using the Substitution Method
Combining Like Radical Terms
Elimination Using Multiplication
Solving Equations
Pythagoras' Theorem 1
Finding the Least Common Multiples
Multiplying and Dividing in Scientific Notation
Adding and Subtracting Fractions
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Adding and Subtracting Fractions
Multiplication by 111
Adding Fractions
Multiplying and Dividing Rational Numbers
Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
Solving Compound Linear Inequalities
Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
Multiplying and Dividing Signed Numbers
Solving Systems of Equations
Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
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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Factoring a Polynomial by Finding the GCF

Example 1

Factor: 9wxy3 - 21w2y4 + 12w3xy2


Step 1 Identify the terms of the polynomial. 9wxy3, - 21w2y4, 12w3xy2
Step 2 Factor each term. 9wxy3

- 21w2y4


= 3 · 3 · w · x · y · y · y

= -1 · 3 · 7 · w · w · y · y · y · y

= 2 · 2 · 3 · w · w · w · x · y · y

Step 3 Find the GCF of the terms.

In the lists, the common factors are 3, w, y, and y.

The GCF is 3 · w · y · y = 3wy2.

Step 4 Rewrite each term using the GCF.

To help keep the signs straight, write the subtraction of 21w2y4 as addition of -21w2y4.

Rewrite each term using 3wy2 as a factor.




9wxy3 - 21w2y4 + 12w3xy2

9wxy3 + (-21w2y4) + 12w3xy2

3wy2 · 3xy + 3wy2 · (-7wy2) + 3wy2 · 4w2x

Step 5 Factor out the GCF.

Factor 3wy2.




3wy2(3xy -7wy2 + 4w2x)


Thus, 9wxy3 - 21w2y4 + 12w3xy2 = 3wy2(3xy -7wy2 + 4w2x)

You can multiply to check the factorization. We leave the check to you.


Another way to decide which terms belong inside the parentheses is to ask:

“3wy2 times what gives 9wxy3?” Answer: 3xy

“3wy2 times what gives -21w2y4?” Answer: -7wy2

“3wy2 times what gives 12w3xy2?” Answer: 4w2x


Example 2

Rewrite 5 - x as a product by factoring out -1.


Identify the terms of the polynomial. 5 and -x
Rewrite each term using -1 as a factor.



= -1 · -5

= -1 · x

We can write:  
Factor out -1-   = -1(-5 + x)
We usually write terms with variables first. So, we use the Commutative Property of Addition to rearrange the terms inside the parentheses.

So we can write 5 - x as -1(x - 5).

We multiply to check the factorization.

  = -1(x - 5)



-1(x - 5)

-1 · x + (-1) · (-5)

- x + 5

= 5 - x ?

= 5 - x ?

= 5 - x ? Yes

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