1. 6.1 Polynomial Functions

2. Polynomials
A polynomial is a sum of terms whose exponents are whole numbers (not fractions or negative numbers).
Polynomials:
y = x3 + 4x2 – 2x + 1
y = x
y = 10
Not Polynomials:

3. Classifying Polynomials
A polynomial is said to be in standard form when the terms are in descending order by degree.
What is the degree of the polynomial? What is the leading coefficient?
y = x3 + 4x2 – 2x + 1

4. Adding Polynomials (8x3 – 3x2 – 2x + 9) + (2x3 + 6x2 – x + 1) =
To add polynomials, just combine like terms:
(8x3 – 3x2 – 2x + 9) + (2x3 + 6x2 – x + 1) =
10x3 + 3x2 – 3x + 10
(12x4 – 5x2 + x + 7) + (2x3 + 6x2 – x + 2) =
12x4 + 2x3 + x2 + 9

5. Subtracting Polynomials
To subtract polynomials, combine like terms. (Just be careful with the signs.)
(8x3 – 3x2 – 2x + 9) - (2x3 + 6x2 – x + 1) =
6x3 - 9x2 – x + 8
(12x4 – 5x2 + x + 7) - (2x3 + 6x2 – x + 2) =
12x4 - 2x3 - 11x2 + 2x + 5

6. Comparing Models
Using a graphing calculator, determine whether a linear model, a quadratic model, or a cubic model best fits the values in the table. X 5 10 15 20 Y
10.1
2.8
8.1
16.0
17.8 X 2 4 6 8 Y
2.8 5
5.5

7. Comparing Models
The table shows data on the number of employees that a small company had from 1975 to Find a cubic function to model the data. Use it to estimate the number of employees in 1998.
Year
Number of Employees
1975 60
1980 65
1985 70
1990
1995 55
2000 64

8. Multiplying Polynomials
This is just FOIL
This is just like FOIL

9. Multiplying Polynomials

10. Multiplying Polynomials

11. Multiplying Polynomials