1. Warm Up Jan. 28th

2. Polynomials A polynomial is a monomial or a sum of monomials
Example: x3 + xy + y2

3. Classifying Polynomials
Types of Polynomials:
Monomial – a #, variable or the product of the two.
Binomial – the sum/difference of two monomials.
“Bi” means 2  like bicycle, has 2 wheels.
example: x2 + 2xy
Trinomial – the sum/difference of three monomials.
“Tri” means 3  like tricycle, has 3 wheels
example: 5a – ab + c4
Polynomials with more than three terms do not have a special name.

4. Monomial, Binomial, Trinomial?
Examples: State whether each expression is a polynomial. If so, identify what type of polynomial.
Expression
Polynomial?
Monomial, Binomial, Trinomial?
1. 2x – 3yz
2. 8n3 + 5n-2
3. -8
4. 6a2 + 3a – a + 11

5. Polynomial Vocabulary
Degree of a monomial – the sum of the exponents of all its variables.
Degree of a polynomial – the greatest degree of any one term in the polynomial. (you must find the degree of each term).
Standard Form of Polynomials- is ordering terms in descending (decreasing) order by degree.

6. Finding Degrees of Monomials5x
8xy
6x3y2
-7y4z 4 11

7. Polynomial in Standard Form
Degrees
Polynomial
Degree
of each
term
Polynomial in Standard Form
Degree of Polynomial
5mn2
-4x2y2 + 3x2 + 5
3a + 7ab – 2a2b + 16
3xy2 – 4x3 + x2y + 6y

8. Name Using Number of Terms
Names Using Degrees
Degree
Name Using Degree
Polynomial Example
Number of Terms
Name Using Number of Terms
Constant 6
Monomial
Linear
x + 4
Quadratic
4x2
Cubic
4x3 – 2x2 + x

9. Examples: Put in standard form and find the degree of the polynomial
1. -2xy2z a + 7ab – 2a2b
h3m + 6h4m2 – 7

10. Write Polynomials in Order
Example 1: Arrange the terms of each polynomial so that the powers of x are in descending order.
3a3x2 – a4 + 4ax5 + 9a2x
2xy3 + y2 + 5x3 – 3x2y

11. Example 2: Arrange the terms of each polynomial so that the polynomial is in Standard Form.
6x2 + 5 – 8x – 2x3
7x2 + 2x4 – 11

12. Homework HW Unit 1 Lesson 3
Tell your parents about Academic Night on Thursday!
January 31st at 5:15 (Media Center)

13. Warm Up Jan. 29th 2013 Is this a polynomial?
Simplify: (-4m2n3)(3mn4)-1
Simplify: 4x – x + 2x – x
Simplify:
State the degree.
a) 42h3 b) 24x4y2 – x2y5 + x3

14. Add & Subtract Polynomials
Adding Polynomials
Hint: combine like terms!
Make sure they have the same variable & exponent.
(4xy + 7x2 – 6y) + (3xy + 2y – 5x2)
We are NOT multiplying or dividing so…
DON’T TOUCH THE EXPONENTS!!!!

15. Example 1: Find the sum of (4x2 + 3x - 7) + (x2 + 10)
2 ways to simplify:
Horizontal Vertical
(4x2 + 3x – 7) + (x2 + 10) (4x2 + 3x – 7)
+ ( x )

16. Watch out for mixed up polynomials
Watch out for mixed up polynomials! Example 2: Find the sum of (7 + 3x2 + 5xy) + (xy – 2x2 + 2)

17. Subtracting Polynomials
Hint: distribute the subtraction sign and combine like terms!
Example 3: Find the difference.
(3x2 + 2x – 6) – (2x + x2 + 3)

18. Example 4: Find the difference.
(5ab2 + 3ab) – (2ab2 + 4 – 8ab)

19. Geometry Application
Example 5: Given the perimeter and the measures of 2 sides of a triangle, find the measure of the third side.
P = 7x + 3y
x – 2y x + 3y

20. Activities! Find a partner and complete the dominoes.
After you get them checked by Mrs. Sawyer—start the Polynomial Search.
IT IS DUE BEFORE THE END OF CLASS!

21. Homework
HW Unit 1 Lesson 4