What is the Rational Roots / Zeros Theorem? When and why do we use it? How does it tie together with Synthetic / Long division and Factor/Remainder Theorems? Finding all possible rational roots, actual rational roots, and all zeros of a polynomial function. Introductory lesson which reviews important foundational skills first, and learning to distinguish whether or not Rational Roots Theorem is necessary in solving a polynomial equation.

This package is a total of 47 PAGES!

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✫ THIS ZIP-FILE IS ALSO INCLUDED IN MY BUNDLES:

1) Entire Polynomials Unit Bundle

2) Long & Synthetic Division and Rational Roots Theorem

✫ CHECK OUT My Related Lessons: Synthetic Division and Rational Root Theorem!

✫ You also might be interested in: Real-World Word Problems [Degree>2 Polynomials]

Related Blogs:

✫ Polynomial Long & Synthetic Division

✫ How to Teach Long/Synthetic Division

Related YouTube Video:

✫ How to Do Long vs Synthetic Division

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This carefully thought-out lesson is unique because it first reviews the FOUNDATION:

[16 Slides]

➤ Vocabulary words: Root/zero, rational number, constant, leading coefficient.

➤ Determining whether or not a number is a zero of a function.

➤ Review of Factor/Remainder Theorems.

➤ How to input a fraction into the Table of Values (changing the Table setting).

➤ Asks students to briefly explain their reasoning; not simply regurgitating the material.

Other information:

➤ Includes Desmos photos of functions that show class solutions; some having multiplicity 2, and others having rational & irrational roots.

➤ Reference sheets reviews:

- Detailed steps of Rational Roots Theorem, long division, and synthetic division

- Vocabulary terms: dividend, divisor, quotient, constant, leading coefficient, etc.

Important Connections: The lessons point out important connections that are easily missed if they are not pointed out to students, such as:

➤ In degree=2 equations, we can solve by factoring or quadratic formula.

➤ But in degree>2 equations, what happens if they are not factorable? This is where Rational Roots Theorem comes in; and we need Long / Synthetic Division as part of our skillset.

➤ The entire purpose of Long / Synthetic division is to convert from standard form to factored form so that we can finally solve for the roots!

INCLUDED:

- Step-by-step answer keys and scaffolded notes to EVERYTHING

- Full lesson [16 slides] - PDF and SmartBoard Versions

- 2 Reference sheets

- 2 Worksheets

Topics in This POLYNOMIALS Unit:

BUNDLE: Entire Polynomials Unit

BUNDLE: Long & Synthetic Division and Rational Roots / Zeros Theorem

1) How to Factor the Polynomial - ALL Methods Step-by-Step

2) Solve Equations by Factoring - Which Methods Do I Use?

3) Introduction, End Behavior, Multiplicity, Roots / Zeros, Graphing

4) Local/Absolute Max/Min Values & Intervals of Increase/Decrease

5) Long Division and Introducing Factor & Remainder Theorems

6) Synthetic Division and Factor & Remainder Theorems [Continued]

7) Rational Roots Theorem

8) Real-World Word Problems [Degree>2 Polynomials]

9) Polynomials UNIT TESTS with Study Guide