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Factoring Special Products & Choosing a Factoring Method

Polynomial Factoring. 1/2/2020. Factoring Special Products & Choosing a Factoring Method. Objectives: factor a special quadratic expression, factor out the GCF first, and then factor the remaining quadratic.

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Factoring Special Products & Choosing a Factoring Method

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  1. Polynomial Factoring 1/2/2020 Factoring Special Products & Choosing a Factoring Method Objectives: factor a special quadratic expression, factor out the GCF first, and then factor the remaining quadratic. Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.

  2. Notes • Steps for Factoring a Quadratic Equation 1) Factor out the GCF (if possible) 2) Set up the Magic X. • ac goes on top, and b goes on bottom • Find the pair that multiplies to equal the top, and adds up to equal the bottom. 3) Set up the Magic T. • Put ax on the top two, and the pair we found for the bottom two. • Treat each side as a fraction and reduce if possible 4) You now have your factors.

  3. Notes Factor. Ex. 1) Factor out GCF. 2) Magic X. - What pair multiplies to equal top and adds to equal the bottom? 3) Magic T. - Reduce? 4) You now have your factors.

  4. Notes Now you try. Factor. Ex. 1) Factor out GCF. 2) Magic X. - What pair multiplies to equal top and adds to equal the bottom? 3) Magic T. - Reduce? 4) You now have your factors.

  5. Notes Factor. Ex. 1) Factor out GCF. 2) Magic X. - What pair multiplies to equal top and adds to equal the bottom? 3) Magic T. Why is this different? - Reduce? What can I put in the middle? 4) You now have your factors.

  6. Notes Now you try. Factor. Ex. 1) Factor out GCF. 2) Magic X. - What pair multiplies to equal top and adds to equal the bottom? Why is this different? 3) Magic T. What can I put in the middle? - Reduce? 4) You now have your factors. Do you see a pattern?

  7. Notes • Difference of Two Squares 1. Must be subtraction. 2. Both terms must be perfect squares. Determine if it the problem is a difference of two squares. Ex. Ex. Ex. Now you try. Ex. Ex. Ex.

  8. Notes Factor. Ex. Ex. Ex. Now you try. Ex. Ex. Ex.

  9. Notes Factor. Ex. 1) Factor out GCF. 2) Magic X. - What pair multiplies to equal top and adds to equal the bottom? 3) Magic T. - Reduce? 4) You now have your factors.

  10. Notes Now you try. Factor. Ex. 1) Factor out GCF. 2) Magic X. - What pair multiplies to equal top and adds to equal the bottom? 3) Magic T. - Reduce? 4) You now have your factors.

  11. Notes Factor. Ex. 1) Factor out GCF. 2) Magic X. - What pair multiplies to equal top and adds to equal the bottom? 3) Magic T. - Reduce? 4) You now have your factors.

  12. Notes Now you try. Factor. Ex. Ex.

  13. Summary You have a difference of ____ squares if both terms are _______ squares and it is a __________ expression. If so, just break up each term and make one parenthesis ________ and the other subtraction. two subtraction perfect addition When first factoring take out the greatest common ______ if possible. After that do the Magic __ and Magic __. Look to see if it is a _________ of two squares to use the short cut. factor X difference T

  14. Ticket Out the Door Complete the Ticket Out the Door without talking!!!!! Talking = time after the bell! Put your NAME on the paper. When finished, turn your paper face DOWN. Factor.

  15. Today’s Homework Rules for Homework • Pencil ONLY. • Must show all of your work. • NO WORK = NO CREDIT • Must attempt EVERY problem. • Always check your answers.

  16. Homework Factor.

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