6.1 Polynomial Functions.

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Presentation transcript:

6.1 Polynomial Functions

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:

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

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

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

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

Comparing Models The table shows data on the number of employees that a small company had from 1975 to 2000. 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

Multiplying Polynomials This is just FOIL This is just like FOIL

Multiplying Polynomials

Multiplying Polynomials

Multiplying Polynomials