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Study Guides > College Algebra

Introduction to Zeros of Polynomials


By the end of this lesson, you will be able to:
  • Evaluate a polynomial using the Remainder Theorem.
  • Use the Factor Theorem to solve a polynomial equation.
  • Use the Rational Zero Theorem to find rational zeros.
  • Find zeros of a polynomial function.
  • Use the Linear Factorization Theorem to find polynomials with given zeros.
  • Use Descartes’ Rule of Signs.
  • Solve real-world applications of polynomial equations

A new bakery offers decorated sheet cakes for children’s birthday parties and other special occasions. The bakery wants the volume of a small cake to be 351 cubic inches. The cake is in the shape of a rectangular solid. They want the length of the cake to be four inches longer than the width of the cake and the height of the cake to be one-third of the width. What should the dimensions of the cake pan be?

This problem can be solved by writing a cubic function and solving a cubic equation for the volume of the cake. In this section, we will discuss a variety of tools for writing polynomial functions and solving polynomial equations.

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  • Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/[email protected]..