- 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 6x3?
|6 and x3
||6 · x3 = 6x3
|2 and 3x3
||2 · 3x3 = 6x3
|-2 and -3x3
||-2 · -3x3 = 6x3
|2x and 3x2
||2x · 3x2 = 6x3
|-2x and -3x2
||-2x · -3x2 = 6x3
|6x and x2
||6x · x2 = 6x3
|-6x and -x2
||-6x · -x2 = 6x3
The above factors are not the only factors:
there are more factors of 6x3.
- 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.
- When you multiply out the result of factoring,
you must get the original expression you're trying to factor.
- The book contains lots of good examples for you to look at.