Algebra II Honors—Day 18

Goals for Today Pick up a whiteboard, marker, and eraser. Show me your homework “Special Binomials” for a homework stamp Warmup Reminder—Test #2 Corrections by Friday Essential Questions Classwork/Homework/Study Guide NOTE—Next test on Monday, Sept. 23

Warmup Factor completely GCF only Sum of Cubes Remember SOAP: S O AP Difference of Two Squares The second factor is a difference of two squares that must be simplified further.

Essential Questions (next two days) How do I factor a polynomial expression? How do I interpret the parts of a factored expression in context of the variables?

Rules for Factoring Polynomials GCF Factor out the GCF. Write it in front and put the remaining factor in one set of parentheses. Then try to simplify the remaining factor. Binomials Difference of Two Squares a 2 -b 2 Factor as (a+b)(a-b) Sum of Cubes a 3 +b 3 Factor as (a+b)(a 2 -ab+b 2 ) Difference of Cubes a 3 -b 3 Factor as (a-b)(a 2 +ab+b 2 ) Trinomials Perfect Square Trinomial a 2 +2ab+b 2 or a 2 -2ab+b 2 Factor as (a+b) 2 or (a-b) 2 Use ac and b to find factors of ac that add up to b Rewrite, then factor by grouping 4-term Polynomials Factor by grouping

Step by Step Is there a GCF? – Yes Factor as the product of the GCF and one other factor—i.e. GCF ∙ (the other factor). Look at the other factor and go to the next step below with it. – No Go the the next step.

Step by Step Is it a binomial? – Yes Is it a difference of two squares? (a 2 -b 2 ) – Yes—Factor as (a+b)(a-b) – No—Go to next step Is it a sum of cubes? (a 3 +b 3 ) – Yes—Factor as (a+b)(a 2 -ab+b 2 ) – No—Go to next step Is it a difference of cubes? (a 3 -b 3 ) – Yes—Factor as (a-b)(a 2 +ab+b 2 ) – No—It can’t be factored. – No Go to the next step.

Step by Step Is it a trinomial? – Yes Do you recognize it as a pattern for a perfect square trinomial? (a 2 +2ab+b 2 ) or (a 2 -2ab+b 2 ) – Yes—Factor as (a+b) 2 or (a-b) 2 – No—Go to next step. Use the ac and b pattern to look for factors. Can you find factors of ac that add up to b? – Yes—Rewrite the equation with those factors, group, and factor. – No—You can’t do anything else. If there’s no GCF, it’s a prime polynomial. – No Go to the next step.

Step by Step Is it a four-term polynomial? – Yes Are there two sets of terms that you can group together that have a common factor? – Yes—Group and factor. – No—If it doesn’t have a GCF, it’s a prime polynomial. – No If it doesn’t have a GCF, it’s a prime polynomial.

More than 4 terms? Try grouping terms with common factors to see if they yield anything that can be factored further. We’ll soon study a method of finding factors for these problems.

Let’s Practice—whiteboards Factor completely the polynomials on the board while you refer to the rules and/or steps. Show me your answers for each group before you go on to the next group.

Homework Handout on factoring polynomials – For a homework stamp tomorrow. #1, 3, 6 on Trinomials Study Guide—Bring any questions about this tomorrow so we can go over them. Test on Monday.