Algebra 2 Tuesday 3-10-15 Discussion/Notes/Guided Practice Assignment Last week we learned… How to factor sum and difference of cubes. We also reviewed basic factoring including difference of squares, perfect square trinomials, the AC method, and Grouping. We learned how to factor by putting them in Quadratic Form first. We then learned how to apply these techniques in order to solve polynomial equations. Today, we will be able to… Understand what the Remainder and Factor Theorems are and how to use them: Apply our knowledge of synthetic division in order to evaluate a polynomial function at a certain x-value Apply our knowledge of synthetic division in order to be able to identify factors of the polynomial We will show we can do this by… Asking and answering questions Completing guided practice problems Working in small groups to complete a practice worksheet Completing an exit ticket To know how well we are learning this, we will look for… Correct answers It is important for us to learn this (or be able to do this) because....  The understanding of properties and theorems, and analyzing the number and types of roots aid in graphing the functions. Many real-world situations that cannot be modeled using linear functions can be approximated using polynomial functions. Tomorrow we will learn about… Applying our knowledge of Chapter 6. Warm-Ups Collect Review of Chapter 6 homework. Discussion/Notes/Guided Practice Section 6.7 The Remainder and Factor Theorems Assignment 6.7 Practice Worksheet (odds only) Students will work in pre-determined groups to complete this assignment. Complete Exit Ticket and turn in before you leave Quiz – Wed 3/11/15 Sections 6.6 & 6.7 only

Warm ups: Use Synthetic Division to divide the following: 𝑓 𝑎 =4 𝑎 2 −3𝑎+6 𝑎−2

How does this answer compare to the one on the previous slide? Remainder Theorem Use substitution to evaluate the following: 𝑓 𝑎 =4 𝑎 2 −3𝑎+6 𝑓(2) How does this answer compare to the one on the previous slide?

Example 1: Synthetic Substitution Use Synthetic Substitution to evaluate the following If 𝑓 𝑥 =3 𝑥 4 −2 𝑥 3 + 𝑥 2 −2, find 𝑓 4 .

Self-Evaluation - Rate each learning target: GUIDED PRACTICE Example 1: Synthetic Substitution Use Synthetic Substitution to evaluate the following If 𝑓 𝑥 =3 𝑥 3 −6 𝑥 2 +𝑥−11, find 𝑓 3 . If g 𝑥 =4 𝑥 5 +2 𝑥 3 + 𝑥 2 −1, find 𝑓 −1 . Self-Evaluation - Rate each learning target: Apply our knowledge of synthetic division in order to evaluate a polynomial function at a certain x-value 4 3 2 1 0

𝑥 4 + 𝑥 3 −17 𝑥 2 −20+32 𝑥−4 4 1 1 -17 -20 32 4 20 12 -32 1 5 3 -8 | 0 𝑥 3 +5 𝑥 2 +3𝑥−8 Factor theorem: The binomial 𝑥−𝑎 is a factor of the polynomial 𝑓(𝑥) if and only if f(𝑎)=0.

Example 2: Use the Factor Theorem Show that 𝑥−3 is a factor of 𝑥 3 +4 𝑥 2 −15𝑥−18. Then find the remaining factors of the polynomial.

Self-Evaluation - Rate each learning target: GUIDED PRACTICE Example 2: Use the Factor Theorem Show that 𝑥−2 is a factor of 𝑥 3 −7 𝑥 2 +4𝑥+12. Then find the remaining factors of the polynomial. Self-Evaluation - Rate each learning target: Apply our knowledge of synthetic division in order to be able to identify factors of the polynomial 4 3 2 1 0

Groups: Move into your pre-determined Groups. Brandon Carrie Shawn Maddie Leila/Mrs. S Mitch Mark* Kourtney Taylor Emme Hunter Emily Wally Savannah Caitlin Trey Chloe Ian Kaitlyn David Gabe* Jhonae* Alexis Quintin* 6.7 Practice Worksheet (odds only) Move into your pre-determined Groups. Group leaders will help walk through problems of their choice, ensuring all groups members are able to successfully complete the assignment.

Exit Ticket Algebra 2 Tues 3/10/15 NAME ____________________________ Use Sythetic Substitution to find 𝑓(−3) and 𝑓(4) for the function 𝑥 2 −5𝑥+10. Given the polynomial 𝑥 3 +7 𝑥 2 +7𝑥−15 and one of its factors 𝑥−1, find the remaining factors. Rate yourself on each problem (Scale of 1 to 4): 1. _________ 2. ________