1. Unit 5 – Quadratic Functions & Complex Numbers Topic: Factoring Polynomials Review

2. Terms you should remember from Algebra 1 (define these in your notes) Polynomial Degree GCF Standard Form Quadratic Equation

3. Factoring By GCF: Things to Remember Factoring is un-distributing (someone’s leaving the party). GCF for variables will always be the LOWEST degree term.

4. Factoring by GCF: Un-distributing Determine GCF of the 3 terms. Divide each term by GCF. FINAL ANSWER!

5. Factoring by GCF: Grouping (must have 4 terms) Group 1 st 2 terms & last 2 terms (be sure to rewrite polynomial in standard form). Factor out the common binomial. Factor GCF from each group to find a common binomial. *You should check your answer here by re-distributing to see if you get the original polynomial.

6. 12x 3 - 9x 2 +20x- 15 Factoring by GCF: Algebraic Punnett Square (must have 4 terms) Build a square with these 4 terms inside (be sure to put them in standard form). Write the resulting factors & check your answer. Work backwards to find proper factors (it’s usually easiest to start with the last term) Watch your signs, & remember we like our leading coefficients to be positive.

7. Factoring “Friendly” Quadratic Trinomials (a = 1) REMINDER: quadratic trinomials factor into 2 binomials Bring down the sign of b in 1 st binomial. Sign of b * sign of c = sign of 2 nd binomial. ( )( )+ + Set up your two binomials & factor x 2. x x Find factors of c whose sum is b. 3 4 *You should always check your answer by multiplying out the factors to see if you get your original quadratic!

8. Factoring “Unfriendly” Quadratic Trinomials (a ≠ 1): Dividing Out a GCF Begin just like factoring a “friendly,” except bring down ax instead of just x. ( )( ) + + 2x2x 2x2x 3 8 Find factors of ac whose sum is b. You should be able to factor a GCF out of one of the binomials (in this case the 2 nd ). We began with an extra “2.” Now we finish by dividing out that extra “2.” 2

9. Factoring “Unfriendly” Quadratic Trinomials (a ≠ 1): Grouping Find factors of ac whose sum is b. Expand the trinomial using those factors to replace b. Group and factor out a common binomial. Write the resulting factors & check your answer.

10. 2x22x2 +3x +8x+12 Factoring “Unfriendly” Quadratic Trinomials (a ≠ 1 ): Punnett Square Find factors of ac whose sum is b. Expand the trinomial using those factors. Set up square with expanded quadratic polynomial. Write the resulting factors & check your answer. Work backwards to find proper factors.

11. JOURNAL ENTRY TITLE: Checking My Understanding: Factoring Polynomials Review Review your notes from this presentation & create and complete the following subheadings in your journal: –“Things I already knew:” Identify any information with which you were already familiar. –“New things I learned:” Identify any new information that you now understand. –“Questions I still have:” What do you still want to know or do not fully understand?

12. Homework Complete the Practice Handout for the next class meeting (A-day, 11/2; B-day, 11/3)