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**Factoring, Difference of Two Squares**

Polynomial Factoring 4/23/2017 Factoring, Difference of Two Squares Objective: factor a quadratic expression where the a term does not equal one. 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.

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Notes Magic X Ex. Ex. Ex. Ex. Ex. Ex.

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**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.

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**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.

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**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.

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**Notes Factor. Ex. 1) Factor out GCF. 2) Magic X.**

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.

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**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.

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**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.

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**Notes Factor. Ex. 1) Factor out GCF. 2) Magic X.**

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.

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**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.

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

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Summary To factor a quadratic first set up the Magic __. On top multiply ac and on _______ put b. Now find a pair of numbers that ________ to equal the top and ____ to equal the bottom. Next set up your ______ T. Put ax on the top and put your pair on the bottom. Reduce if possible. X bottom multiply add Magic 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 perfect subtraction addition

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**Class Work / Homework Rules for Homework Pencil ONLY.**

Must show all of your work. NO WORK = NO CREDIT Must attempt EVERY problem. Always check your answers.

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Class Work / Homework Factor.

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