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Math
Elementary Algebra
Polynomials

Polynomials

We have seen that the graphs of linear equations are straight lines. Graphs of other types of equations, called polynomial equations, are curves, like the outline of a suspension bridge. Architects use polynomials to design the shape of a bridge like this and to draw the blueprints for it. Engineers use polynomials to calculate the stress on the bridge’s supports to ensure they are strong enough for the intended load. In this chapter, you will explore operations with and properties of polynomials.

Sections

  • Add and Subtract Polynomials — identifying polynomials, monomials, binomials, and trinomials; determining the degree of polynomials; adding and subtracting monomials and polynomials; and evaluating a polynomial for a given value.
  • Use Multiplication Properties of Exponents — simplifying expressions with exponents, and using the product, power, and product-to-a-power properties of exponents together.
  • Multiply Polynomials — multiplying a polynomial by a monomial, multiplying two binomials (Distributive, FOIL, and Vertical methods), multiplying a trinomial by a binomial.
  • Special Products — squaring a binomial using the Binomial Squares pattern, and multiplying conjugates using the Product of Conjugates pattern.
  • Divide Monomials — simplifying expressions using the Quotient Property of Exponents, the Zero Exponent Property, and the Quotient to a Power Property, and dividing monomials.
  • Divide Polynomials — dividing a polynomial by a monomial and dividing a polynomial by a binomial.
  • Integer Exponents and Scientific Notation — using the definition of a negative exponent, simplifying expressions with integer exponents, converting between decimal and scientific notation, and multiplying and dividing in scientific notation.

This chapter overview is adapted from Elementary Algebra 2e, Chapter 6 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.

Knowledge Check: Chapters 1–5Add and Subtract Polynomials