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Algebra II Honors—Day 18

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.

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Algebra II Honors—Day 18

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  1. Algebra II Honors—Day 18

  2. 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

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

  4. 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?

  5. Rules for Factoring Polynomials

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

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