1. In this lesson we will classify, add and subtract polynomials.

2. We can write 3a2b like this..
A monomial is a number, a variable or a product of numbers and variable(s).
3a2b is a monomial
We can write 3a2b like this..
3 · a · a · b

3. A polynomial is a monomial or the sum of two or more monomials
3a2b + 6a is a polynomial
Each monomial in a polynomial is called a TERM

4. A polynomial can be classified by the number of terms
A polynomial with 1 term is a monomial
5xy3
A polynomial with 2 terms is a binomial
3x + y3
A polynomial with 3 terms is a trinomial
2x2 + 3x –1

5. We can also classify polynomials by the highest exponent in the polynomial which is the degree of the polynomial
The degree of 3x2 is 2
The degree of 5x + 3 is 1
The degree of 4x3 – 2x2 + 9 is 3

6. Classify the polynomial by the number of terms
7m3 + 2m
This polynomial contains two monomials.
This is a binomial

7. Classify this polynomial by degree
3x2 – 8x + 12
The first term in the polynomial has an exponent of 2 which is the highest exponent in the polynomial
The polynomial is degree 2

8. We can model polynomials with algebra tiles
2x2 – 3x + 4

9. Add the two polynomials
(x2 – 2x + 2) + (2x2 + 3x – 5)
First model the polynomials
Now add like terms

10. The result is 3x2 + x – 3
(x2 – 2x + 2) + (2x2 + 3x – 5)

11. Start by modeling each polynomial with tiles
To subtract polynomials first use the distributive property which changes the sign for each term in the polynomial that is subtracted
(2x2 + 2x – 1) – (x2 – x – 3)
Start by modeling each polynomial with tiles

12. Here is the model for each polynomial
(2x2 + 2x – 1) – (x2 – x – 3)
Use the distributive property
2x2 + 2x – 1 – x2 + x + 3

13. Finally, add like terms
2x2 + 2x – 1 – x2 + x + 3
x2 + 3x + 2

14. Complete Activity 9a
Classify Polynomials by the number of terms
Classify Polynomials by degree
Model Polynomials
Add and Subtract Polynomials