Algebra and Trigonometry, 5th Edition

4.1 Polynomial Functions and Models

• Determine the behavior of the graph of a polynomial function using the leading-term test.

• Factor polynomial functions and find their zeros and their multiplicities.

• Solve applied problems using polynomial models.

There are many different kinds of functions. The constant, linear, and quadratic functions that we studied in Chapters 1 and 3 are part of a larger group of functions called polynomial functions.

Polynomial Function

A polynomial function P is given by

$$P(x)=a_n{x}^n+a_{n-1}{x}^{n-1}+a_{n-2}{x}^{n-2}+\cdots +a_{1}x+a_0,$$

where the coefficients $a_n,a_{n-1},\dots ,a_1,a_0$ are real numbers and the exponents are whole numbers.

JUST IN TIME 10

The first nonzero coefficient, $a_n$, is called the leading coefficient. The term $a_n{x}^n$ is called ...