Site US and Canada

Exploring Polynomials: Factors, Roots, and Zeros

Published on 08/31/2011

Activity Overview

Investigate graphical and algebraic representations of a polynomial function and its linear factors.

Objectives

  • Students will discover that the zeros of the linear factors are the zeros of the polynomial function.
  • Students will discover that the real zeros of a polynomial function are the zeros of its linear factors.
  • Students will determine the linear factors of a quadratic function.
  • Students will connect the algebraic representation to the geometric representation.
  • Students will see the effects of a double and/or triple root on the graph of a cubic function.
  • Students will see the effects of the leading coefficient on a cubic function.
  • Students will look for and make use of structure (CCSS Mathematical Practice).
  • Students will look for and express regularity in repeated reasoning (CCSS Mathematical Practice).

Vocabulary

  • Zeros
  • Double or triple root
  • Leading coefficient

About the Lesson

This lesson merges graphical and algebraic representations of a polynomial function and its linear factors. As a result, students will:

  • Manipulate the parameters of the linear functions and observe the resulting changes in the polynomial function.
  • Find the zeros of the polynomial equations by finding the zeros of the linear factors.