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Algebra 2 5-5 Complete Lesson: Theorems About Roots of Polynomial Equations

By Matt Richardson
Last updated over 3 years ago
22 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! I am greater than my square. The sum of my numerator and denominator is 5. What fraction am I?

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It?

Problem 4 Got It?
HINT: you will need to multiply factors derived from the given roots, including (x - (2 - 3i)) and (x - (2 + 3i)).

Problem 5 Got It? Identify the statements that can be made using Descartes' Rule of Signs regarding the function.

  • There is one negative real root.
  • There are two negative real roots.
  • There are one or three positive real roots.
  • There are two or four positive real roots.
  • According to Descartes' Rule of Signs:

Problem 5 Got It? Reasoning: Can you confirm real and complex roots graphically? Explain. Identify the true statements below.

Vocabulary: Drag a complex number from the left to create a conjugate pair.

Reasoning: In the statement below, r and s represent integers. Is the statement always, sometimes, or never true?

Reasoning: In the statement below, r and s represent integers. Is the statement always, sometimes, or never true?

Review Lesson 5-4: Match each expression on the left with its quotient on the right.

Review Lesson 5-1: Consider the standard form of each polynomial. Then classify it by its degree AND number of terms.

  • monomial
  • binomial
  • trinomial
  • polynomial of four terms
  • constant
  • linear
  • quadratic
  • cubic
  • quartic
  • quintic

Use Your Vocabulary: True or False? 1 and -1 are roots of the equation.

Use Your Vocabulary: True or False? The equation has roots 4 and -4.

Use Your Vocabulary: Identify the number of roots each polynomial has.

  • 1
  • 2
  • 4
  • 6
  • 7
  • 8

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success