Polynomials and Polynomial Functions

You may have coins and paper money in your wallet, but you may soon want to acquire a type of currency called bitcoins. They exist only in a digital wallet on your computer. You can use bitcoins to pay for goods and services at some companies, or save them as an investment. Although the future of bitcoins is uncertain, investment brokers are beginning to investigate ways to make business predictions using this digital currency. Understanding how bitcoins are created and obtained requires an understanding of a type of function known as a polynomial function. In this chapter you will investigate polynomials and polynomial functions and learn how to perform mathematical operations on them.

Sections

• Add and Subtract Polynomials — determining the degree of polynomials, adding and subtracting polynomials, evaluating a polynomial function for a given value, and adding and subtracting polynomial functions.
• Properties of Exponents and Scientific Notation — simplifying expressions using the properties of exponents (product, power, quotient, zero exponent, and negative exponent rules), converting between decimal notation and scientific notation, and multiplying and dividing in scientific notation.
• Multiply Polynomials — multiplying a polynomial by a monomial, multiplying a binomial by a binomial (FOIL), multiplying a trinomial by a binomial, and multiplying polynomial functions.
• Dividing Polynomials — dividing a polynomial by a monomial, dividing polynomials using long division, dividing polynomials using synthetic division, dividing polynomial functions, and using the Remainder and Factor Theorems.

This chapter overview is adapted from Intermediate Algebra 2e, Chapter 5 Introduction by Lynn Marecek and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: condensed the chapter introduction and recast the chapter outline as a section list.