 Finding the Greatest Common Factor (GCF) of Terms
 Given a term c, if a · b = c then a and b are factors of c.

Example: What are some factors of the term 6x^{3}?

Factors

Because...

6 and x^{3}

6 · x^{3} = 6x^{3}

2 and 3x^{3}

2 · 3x^{3} = 6x^{3}

2 and 3x^{3}

2 · 3x^{3} = 6x^{3}

2x and 3x^{2}

2x · 3x^{2} = 6x^{3}

2x and 3x^{2}

2x · 3x^{2} = 6x^{3}

6x and x^{2}

6x · x^{2} = 6x^{3}

6x and x^{2}

6x · x^{2} = 6x^{3}


The above factors are not the only factors:
there are more factors of 6x^{3}.

 The greatest common factor (GCF) of two or more expressions is the greatest factor that divides into (without remainder) each expression.
 The GCF of a bunch of terms contains the lowest power of the variable common to all the terms.
 Steps to Factoring a Monomial from a Polynomial
 Determine the GCF of all terms in the polynomial.
 Write each term as the product of the GCF and another factor.
 Use the distributive property to factor out the GCF.
 The first step in any factoring problem is to factor out the GCF.
 Factoring a 4 Term Polynomial by Grouping
 Arrange the 4 terms into 2 groups of 2 terms each so that each group of 2 terms has a GCF.
 Factor the GCF from each group of 2 terms.
 If the two, new terms formed by step 2 have a GCF, then factor it out.
 Checking
 When you multiply out the result of factoring,
you must get the original expression you're trying to factor.
 Examples
 The book contains lots of good examples for you to look at.
