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 completely22 24 xyyx

63 278 yx

44 16yx

)2(2 yxxy

)964)(32( 4222 yxyxyx

)2)(2)(4(

)4)(4(22

2222

yxyxyx

yxyx

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 PolynomialsGCF

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

a2-b2

Factor as (a+b)(a-b)

Sum of Cubesa3+b3

Factor as(a+b)

(a2-ab+b2)

Difference of Cubes

a3-b3

Factor as (a-b)

(a2+ab+b2)

Trinomials

Perfect Square Trinomial

a2+2ab+b2 or a2-2ab+b2

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 groupin

g

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? (a2-b2)

– Yes—Factor as (a+b)(a-b)– No—Go to next step

• Is it a sum of cubes? (a3+b3)– Yes—Factor as (a+b)(a2-ab+b2)– No—Go to next step

• Is it a difference of cubes? (a3-b3)– Yes—Factor as (a-b)(a2+ab+b2)– 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? (a2+2ab+b2) or (a2-2ab+b2)– 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.