1. Bell ringer Simplify the following expressions as much as you can!
𝑥 4 − 3𝑥 2 + 2𝑥 4 − 5𝑥 3 +4
3𝑥 3 + 7𝑥 2 + 4𝑥 4 + 𝑥 3 −20
Write your final answers in standard form (think of standard form for quadratics!)

2. Polynomials
October 27, 2015

3. Parts of a Polynomial
DEGREES
2𝑥 4 − 5𝑥 3 +4
TERMS

4. Degrees of a polynomial
The power of x helps you classify the polynomial and graphs. Look at the highest power!
𝑥 2 - squared
𝑥 3 - CUBIC
Think of your prefixes for the next ones…
𝑥 4 -
𝑥 5 -
QUARTIC!!
QUINTIC!!

5. Standard form Combines any like terms
Arranges the terms of polynomial by their degree from greatest to least
𝑥 4 − 3𝑥 2 + 2𝑥 4 − 5𝑥 3 +4
3𝑥 4 − 3𝑥 2 − 5𝑥 Combine like terms
3𝑥 4 − 5𝑥 3 − 3𝑥 write degrees in order

6. Write each polynomial in standard form and classify it
3𝑥+ 9𝑥 2 +5
4𝑥− 6𝑥 2 + 𝑥 𝑥 2 −12
3− 4𝑥 5 + 2𝑥 2 + 3𝑥 5 +10
9𝑥 2 +3𝑥+5;𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 2;𝑞𝑢𝑎𝑑𝑟𝑎𝑡𝑖𝑐
𝑥 4 + 4𝑥 2 +4𝑥−12
𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 4;𝑞𝑢𝑎𝑟𝑡𝑖𝑐
−𝑥 5 + 2𝑥 2 +13
𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 5;𝑞𝑢𝑖𝑛𝑡𝑖𝑐

7. End behaviors 𝑦= −𝑥 2 +6𝑥 𝑦= −0.3𝑥 3 +4𝑥+2 𝑦= 𝑥 4 − 3𝑥 3 +5𝑥 𝑦= 𝑥 3
Look at the graphs of the following equations. Predict and conclude the rule for end behavior
𝑦= −0.3𝑥 3 +4𝑥+2
𝑦= 𝑥 4 − 3𝑥 3 +5𝑥
𝑦= 𝑥 3
𝑦= −2𝑥 4 + 8𝑥 3 − 8𝑥 2 +2

8. End behavior rule
If the degree is even: ________________________________
If the degree is odd: _________________________________
If the leading coefficient is negative: ___________________
Each end goes in the same direction
Each end goes in the opposite direction
If degree is even, both ends go down
If odd, left end up, right end down

9. Maximum number of turns
𝑦= −𝑥 2 +6𝑥
Look at the graphs of the following equations. Predict and conclude the rule for the maximum number of turns.
𝑦= −0.3𝑥 3 +4𝑥+2
𝑦= 𝑥 4 − 3𝑥 3 +5𝑥
𝑦= 𝑥 3
𝑦= −2𝑥 4 + 8𝑥 3 − 8𝑥 2 +2

10. Maximum number of turns rule
What did you come up with?
Max # of turns: Highest degree – 1

11. Partner Work/Homework
Workbook page 47 #1, 2, 4, 8-11