Algebra and Trigonometry, 5th Edition

Chapter 4 Summary and Review

Study Guide

KEY TERMS AND CONCEPTS	EXAMPLE
SECTION 4.1: POLYNOMIAL FUNCTIONS AND MODELS
Polynomial Function $$\begin{array}{rcl}P(x)& =& a_n{x}^n+a_{n-1}{x}^{n-1}+a_{n-2}{x}^{n-2}\\ +\cdots +a_{1}x+a_0,\end{array}$$ where the coefficients $a_n,{\text{ a}}_{n-1},\dots ,{\text{ a}}_1,{\text{ a}}_0$ are real numbers and the exponents are whole numbers. The first nonzero coefficient, $a_n$, is called the leading coefficient. The term $a_n{x}^n$ is called the leading term. The degree of the polynomial function is n. Classifying polynomial functions by degree: Type Degree Constant 0 Linear 1 Quadratic 2 Cubic 3 Quartic 4	Consider the polynomial $$P(x)=\frac{1}{3}{x}^2+x-4x^5+2.$$ Leading term: $-4x^5$ Leading coefficient: −4 Degree of polynomial: 5 Classify the following polynomial functions: Function Type $f(x)=-2$