1. Combine Like Terms 3x – 6 + 2x – 8 3x – 7 + 12x + 10
Warm-up
Combine Like Terms
3x – 6 + 2x – 8
3x – x + 10
10xy + 5y – 6xy – 14y
5x – 14
15x + 3
4xy – 9y

2. Sum and Product Puzzles 56 30 9 -6 18 13
Find two numbers that multiply to get the top number and add together to get the bottom number.

3. How do we name, add, and subtract polynomials?
Math I
UNIT QUESTION: In what ways can algebraic methods be used in problems solving?
Standard: MM1A2
Today’s Question:
How do we name, add, and subtract polynomials?
Standard: MM1A2c

4. Adding and Subtracting Polynomials
MONOMIALS:
A monomial is _______________
____________________________
______________________
 Some examples of monomials are:
a number, variable, or a product of numbers and variables.
x y a5

5. POLYNOMIALS:
 A polynomial is the ___________ or _________ of monomials.
monomial
the sum
 An example of a polynomial in one variable, x, would be x3 + 6x2 + 12x + 8
 How many MONOMIALS are there in the above polynomial? 4

6.  The largest exponent in the polynomial determines the DEGREE OF A POLYNOMIAL.
 Example: The degree of 9 – 7x – 4x2 is ____ because ____the largest exponent in the polynomial.
Example: Find the degree of the following polynomial:
x4 + 6x3 + 7x5 + 12x 5

7. STANDARD FORM
 The terms of a polynomial are in STANDARD FORM if they are ordered from left to right in ______________ order; which means from the LARGEST exponent to the smallest.
decreasing
 The coefficient of the first term is called the ______________________.
leading coefficient
Example – Write this in standard form: x4 + 6x3 + 7x5 + 12x
What is the leading coefficient?

8. decreasing – 4x3 + x + 9 – 5x3 + 3x2 + 4x - 2
STANDARD FORM
 To write a polynomial in Standard Form, arrange the terms of the polynomial in ______________ order according to the exponent of the variables.
decreasing
 Example: Write 9 + x – 4x3 in standard form.
– 4x3 + x + 9
 Example: Write 3x2 – 2 + 4x – 5x3 in standard form.
– 5x3 + 3x2 + 4x - 2

9. In your own notes:

10. Some polynomials have SPECIAL NAMES that are determined by the following:
Their __________ or
Their __________ of terms
Draw the following Charts in YOUR notes.
degree
number

11. # of Terms
Name by # of Terms
Monomial
Binomial
Trinomial
4+ Polynomial

12. Degree Name by degree 0 Constant 1 Linear 2 Quadratic 3 Cubic
(largest exponent)
Name by degree
Constant
1 Linear
Quadratic
3 Cubic

13. Now, back to the WS

14. 12 8x 4x2 + 3 5x3 + x2 3x2 – 4x + 6 Polynomial Name by # of Terms
DEGREE
Name by Degree 12 8x
4x2 + 3
5x3 + x2
3x2 – 4x + 6
Monomial Constant
Monomial Linear
Binomial 2 Quadratic
Binomial Cubic
3 Trinomial 2 Quadratic

15. Now, a few examples to add to YOUR notes:

16. Special Names:
Degree Name: # of Terms Name:
Linear
Binomial

17. Special Names:
Degree Name: # of Terms Name:
Cubic
Monomial

18. Special Names:
Degree Name: # of Terms Name:
Quadratic
Binomial

19. Special Names:
Degree Name: # of Terms Name:
Cubic
Trinomial

20. Adding Polynomials
Back to your WS

21. drop the parenthesis and combine like terms
 When adding polynomials _________________________________________________________
drop the parenthesis and combine like terms

22. Example
5a2 – 2b2

23. 1.
3x2 + x + 2

24. 2.
x2 + 2x – 2

25. 3.
-2x2 + 3x – 5

26. 4.
-x + 6

27. Back to your notes
When SUBTRACTING polynomials Drop the 1st parenthesis then distribute the NEGATIVE to the 2nd parenthesis.

28. 3a a – 8a2 + a
– 5a2 + 11a

29. 7x – 3 – 9x + 2
– 2x – 1

30. 3x2 + 2x – 4 – 2x2 – x + 1
x2 + x – 3

31. Class Work
Red Workbook p. 61
Lesson Practice 2.1
#16 – 23

32. Home Work
Textbook p. 61
#1 – 14