January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29, 2015
Algebra 1
7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping
Homework #14, Pg.467, #1­53 odd (27 Points, Due January 30)
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
To factor means to rewrite an expression as a product.
There are many methods to factoring polynomials. The first method we'll learn is to factor by using the GCF of the polynomial.
Step 1: Identify the GCF of the polynomial. This is often done mentally, though you can do this on paper if you need to.
Step 2: Rewrite the polynomial as
Step 3: Simplify the ratios inside the quantity. As you practice more and more, Step 2 and Step 3 will be combined.
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
Practice factoring these on your own
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
Sometimes the GCF of a polynomial is a binomial. This GCF is called a common binomial factor or a common quantity. You factor out common quantities in the same was as you factor out a monomial GCF.
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
When a polynomial has four terms, you can make two groups and factor out the GCF from each group (if one exists).
Always make sure your polynomial is written in descending order (standard form)
Step 1: Group two terms on each side
Step 2: Factor the GCF from each side. This may result in a common quantity being shared by both sides.
Step 3: Finish factoring like normal.
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015
Recognizing opposite binomials can help you factor polynomials. The binomials (a ­ b) and (b ­ a) are opposites. If you have a difference­binomial, (a ­ b), and you want to switch the order of the terms, factor out a negative 1:
This is helpful when you're looking to make common quantities.
January 29 ­ 7.2 Factoring by using the Greatest Common Factor and Factoring by Grouping.notebo
January 30, 2015