1. DO NOW : Simplify 1. -9b + 8b 2. 6y – y 3. 4m + (7 - m)
4. c – (3c + 1)
5. (3r + 4) + (-2r + 8)
6. (-2g + 1) – (2g + 1)
7. (5j – 7k) – ( 4j – 6k)
Answers: -b, 5y, 3m + 7, -2c-1, r+12, -4g, j-k

2. Adding & Subtracting Polynomials

3. Essential Question How do I classify polynomials?
How do I add and subtract polynomials?

4. Definitions Polynomial: monomial, or a sum or difference of monomials.
Degree of a polynomial: exponent with the greatest value within the polynomial
Standard form (of a polynomial): left to right, in descending order, greatest exponent to the least.

5. Definitions Monomial: one term polynomial
Binomial: two term polynomial
Trinomial: three term polynomial
Use the word Polynomial to describe 4 or more terms

6. Classifying Polynomials by Degree
Degree 0: CONSTANT
Degree 1: Linear
Degree 2: Quadratic
Degree 3: Cubic
Degree 4: 4th
Degree 5: 5th
Degree 6 or higher: nth degree, where n is the degree #

7. Writing polynomials in standard form
Combine like terms
Then write terms in order starting with the highest exponent.
The constants (#s without variables) come last!
Ex: -4x2 + x3 + 3
Standard Form: x3 - 4x2 + 3

8. You try. Write 9 – 3m2 – m3 + 2m in standard form. Answer:
Remember to order your exponents from greatest to least. Always separate your terms by a (+) or (-) sign.

9. Special names for polynomials:
# terms
Name
degree 12 1
Monomial 8x
4x2 + 3 2
Binomial
5x3 + x2 3
3x2 – 4x+6
Trinomial
3x4-4x3+6x2-7 4
polynomial

10. Example 1 (3x2 +4x-2) + (5x2 - 6x - 8) Group like terms and subtract.

11. Example 2 Subtract 15x – 4 from 2x2 + 11x.
Distribute the negative
Group like terms and subtract.
2x2 + 11x – (15x – 4)
= 2x2 + 11x –15x + 4
= 2x2 – 4x + 4

12. Example 3 Find the difference. (-2x3 + 5x2 – x + 8) – (-2x3 + 3x – 4)

13. Example 5 Using the vertical form to add and subtract polynomials.
Add 12y3 + y2 – 8y + 3 and 6y3 – 13y + 5.
Align like terms and add.
12y3 + y2 – 8y + 3 +
6y3 – 13y + 5
18y3 + y2 – 21y + 8

14. Use the vertical format to Subtract:
(4x2+3x+2) – ( 2x2-3x+7)
4x x x x +2
- (2x2 -3x ) -2x x +
2x2 + 6x - 5

15. Example 6
Find the difference.
(x2 – 8) – (7x + 4x2)

16. Practice A. Find the sum: (3x2 + 5x) + (4 – 6x – 2x2) B.
Subtract: (3x2 – 2x +3) – (x2 + 2x – 4)
Answers: x2 – x + 4, x2 – 4x + 7

17. Summarizer How do you determine the degree of a polynomial?
Classify 3x5+4x2-7 in two different ways. (What is it specifically called? What is the degree of the polynomial?)
Degree of a polynomial is the highest degree within.
5th degree, Trinomial

18. Classwork Homework In textbook: p. 61 # 7 – 12 and p. 62 # 4 – 9
Adding and Subtracting Wkst & Did You Hear Wkst
Homework
In textbook: p. 61 # 7 – 12 and
p. 62 # 4 – 9