# 7.7 Chapter Summary

In this chapter, we studied polynomials and their algebraic properties.

Page Summary
Introduction We can generalize linear functions, which are functions that have x's and constants that are added together, and quadratic functions, which are functions that have x2's, x's, and constants added together, to mathematical creatures with higher and higher powers of x's. In general, these types of mathematical creatures are known as polynomials.
What is a Polynomial? A mathematical creature of the form:

P(x)=c_{n}x^n+c_{n-1}x^{n-1}+\cdots c_{2}x^2 + c_{1}x^1 + c_{0}x^0
is called a polynomial of degree n. Each of the ci's are real numbers with the leading coefficient, cn≠0.
The Basic Shape of a Polynomial The basic shape of f(x)=xeven powers is

The basic shape of f(x)=xodd powers is
Adding Polynomials To add two polynomials, combine the x terms with the same powers, adding the coefficients.
Multiplying Polynomials To multiply two polynomials, we multiply each term of the first polynomial by each term in the second polynomial, then combine all terms with the same powers.

Key Points