Skip to main content
Mathematics LibreTexts

6: Exponents and Polynomials

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Learning Objectives

    By the end of this chapter, the student should be able to

    • Simplify exponential expressions with positive and/or negative exponents
    • Multiply or divide expressions in scientific notation
    • Evaluate polynomials for specific values
    • Apply arithmetic operations to polynomials
    • Apply special-product formulas to multiply polynomials
    • Divide a polynomial by a monomial, applying long division, synthetic division

    In order to apply more involved properties to polynomials, we first discuss a variety of properties of exponents. Problems with exponents can often be simplified using a few basic exponent properties. Exponents represent repeated multiplication and we can use this fact to discover the properties of exponents.


    The word exponent comes from the Latin “expo” meaning out of, and “ponere” meaning to place. While there is some debate, it seems that the Babylonians living in Iraq were the first to do work with exponents dating back to the \(23^{\text{rd}}\) century BC or earlier.

    This page titled 6: Exponents and Polynomials is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.