Unit 3, Polynomial Functions: Day 6 (BI, Chapter 4, Section 4)

Focus: Factoring Polynomials

Action Items:

1. Warm Ups

2. Show me HW 3.5

3. Notes and practice factoring polynomials using a variety of methods (see notes below).

4. HW 3.6: BI p. 184 #5-6, and 8-12 all; and #33-41 odd (as always WTP and SYS).

Notes on Factoring Polynomials

The process of Factoring Polynomials uses the same strategies we used to factor quadratics, and extends them:

GCF! Always check for a greatest common factor first -- and not just the numbers! Always check to see if there is an "x" in every term!
Apply the "Quadratic Form (Structure)" to polynomials of higher (even) degree
- Example: you can factor $LaTeX: x^2+7x+12=\left(x+3\right)\left(x+4\right)$ --> --> so you can also factor $LaTeX: x^4+7x^2+12=\left(x^2+3\right)\left(x^2+4\right)$ . Look carefully to see what is the same and be sure you understand why!
Special Products (Difference of Squares with higher powers)

Just as with quadratics, when we divide polynomials, we are factoring them. We want to be able to factor polynomials for the same reason we wanted to be able to find the factors of quadratics: if you can factor a polynomial, you can set the factors equal to zero and then use the ZPP (zero product property) to find the x - intercepts of the polynomial. This will help us when we use polynomials to model problems in applications and will help us with graphing as well.

Introduction to Factoring & Solving Polynomials: Ppt

Polynomials Unit Resources

Polynomials Unit Homework Solutions