Section 6 1 Polynomial Functions Exploring Polynomial Functions

Section 6. 1 Polynomial Functions

Exploring Polynomial Functions Definition 1: A polynomial is a monomial or the sum of monomials. Definition 2: An exponent of the variable in a term determines the degree of that term. Definition 3: This order demonstrates the standard form of a polynomial. Definition 4: The degree of a polynomial is the largest degree of any term of the polynomial.

Polynomial Functions Degree Name Using Degree Polynomial Example Number of Terms Name Using Number of Terms

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

TOTD Write each polynomial in standard form. Then classify it by degree and number of terms. 9 + x³ x - 2 x² - 3 x³

Example 9

Example 10

Example 11

Example 12 Gold The table below shows world gold production for several years. Find a quartic function to model the data. Use it to estimate production in 1988.

Example 13 Vital Statistics The data below indicates that the life expectancy for residents of the U. S. has been increasing. Find quadratic models for the data set. Find cubic models for the data set. Graph each model. Compare the quadratic and cubic models to determine whether one is a better fit.

TOTD Simplify. Classify the result by number of terms. (7 x² + 8 x – 5) + (9 x² - 9 x) Find each product. Classify the result by number of terms. (x+ 3)(4 x – 1)(3 x + 7)