Polynomials

Expressions known as polynomials are used widely in algebra. Applications of these expressions are essential to many careers, including economists, engineers, and scientists. In this chapter, we will find out what polynomials are and how to manipulate them through basic mathematical operations.

Sections

• Add and Subtract Polynomials — identifying polynomials, monomials, binomials, and trinomials, determining the degree of a polynomial, adding and subtracting monomials and polynomials, and evaluating a polynomial for a given value.
• Use Multiplication Properties of Exponents — using the product, power, and product-to-a-power properties of exponents, and simplifying expressions using a combination of these properties.
• Multiply Polynomials — multiplying a polynomial by a monomial, multiplying a binomial by a binomial, and multiplying a trinomial by a binomial.
• Divide Monomials — simplifying expressions using the quotient property of exponents, the zero exponent property, and the quotient to a power property, and dividing monomials.
• Integer Exponents and Scientific Notation — using the definition of a negative exponent, converting between scientific notation and decimal form, and multiplying and dividing numbers written in scientific notation.
• Introduction to Factoring Polynomials — finding the greatest common factor of two or more expressions, and factoring the greatest common factor from a polynomial.

This chapter overview is adapted from Prealgebra 2e, Chapter 10 Introduction by Lynn Marecek, MaryAnne Anthony-Smith, 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.