Unit 5 – Quadratic Functions & Complex Numbers

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

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

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

6. 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). 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. Write the resulting factors & check your answer.

7. Factoring “Friendly” Quadratic Trinomials (a = 1) • REMINDER: quadratic trinomials factor into 2 binomials Set up your two binomials & factor x2. Bring down the sign of b in 1stbinomial. Sign of b * sign of c = sign of 2ndbinomial. x + x ( )( ) + 4 3 Find factors of c whose sum is b. *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. ( )( ) 2x + 8 2x + 3 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 2nd). 2 We began with an extra “2.” Now we finish by dividing out that extra “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. 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. Work backwards to find proper factors. Write the resulting factors & check your answer.

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