Description
✫ THIS PACKAGE INCLUDES 139 QUALITY PAGES!!
LESSONS 1 & 2: ➤ Long Division of polynomials step-by-step reference sheets and examples that begin from easy elementary school-level with numbers, and work their way up to long division of polynomials; ranging from beginner to challenging. Factor and Remainder Theorems; students practice the steps of dividing polynomials using long division, especially with remainders that do not equal zero, and students review how to write the answer (quotient + remainder/divisor).
LESSON 3: ➤ Step-by-step Synthetic Division of polynomials and relationship to remainder/factor theorems. Many examples and important connections of how synthetic division (and long division) ties into the big picture, ultimately finding zeros/roots of polynomials. Important vocabulary such as dividend, quotient, divisor, and remainder. Synthetic division worksheet, reference sheets, full lesson, answers and scaffolded notes!
LESSON 4: ➤ 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.
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✫ CHECK OUT MY ENTIRE POLYNOMIALS UNIT BUNDLE!
Related Blogs:
✫ Polynomial Long & Synthetic Division
✫ How to Teach Long/Synthetic Division
Related YouTube Video:
✫ How to Do Long vs Synthetic Division
----------------------------------------------------
OTHER NOTES:
➤These carefully thought-out lesson is unique because it first reviews the FOUNDATION:
- 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.
➤ 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 or Synthetic Division as part of our skillset.
➤ The entire purpose of Long or Synthetic division is to convert from standard form to factored form so that we can finally solve for the roots!
➤ The lessons tie together WHY students would care about Synthetic Division (and Long Division); which is because it is one of the steps in Rational Roots Theorem in order to ultimately solve for the roots/zeros of a polynomial equation. This is just one of many important connections included in this lesson that students often miss because the information is not compartmentalized in the way that it needs to be so that they can see the big picture.
➤ There is an important example where students can use synthetic division to divide (x^3 - 64) by (x-4) to convert the degree=3 polynomial into factored form... and students will see that they can use the Difference of Perfect Cubes formula to confirm that this works!
➤ 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.
INCLUDED:
- 4 Full Lessons [68 Slides] - PDF & SmartBoard Versions
- 2 Detailed Reference Sheets
- 5 Worksheets
Long / Synthetic Division & Rational Roots Theorem | Lessons, Worksheets, Keys
Highlights
Description
✫ THIS PACKAGE INCLUDES 139 QUALITY PAGES!!
LESSONS 1 & 2: ➤ Long Division of polynomials step-by-step reference sheets and examples that begin from easy elementary school-level with numbers, and work their way up to long division of polynomials; ranging from beginner to challenging. Factor and Remainder Theorems; students practice the steps of dividing polynomials using long division, especially with remainders that do not equal zero, and students review how to write the answer (quotient + remainder/divisor).
LESSON 3: ➤ Step-by-step Synthetic Division of polynomials and relationship to remainder/factor theorems. Many examples and important connections of how synthetic division (and long division) ties into the big picture, ultimately finding zeros/roots of polynomials. Important vocabulary such as dividend, quotient, divisor, and remainder. Synthetic division worksheet, reference sheets, full lesson, answers and scaffolded notes!
LESSON 4: ➤ 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.
----------------------------------------------------
✫ CHECK OUT MY ENTIRE POLYNOMIALS UNIT BUNDLE!
Related Blogs:
✫ Polynomial Long & Synthetic Division
✫ How to Teach Long/Synthetic Division
Related YouTube Video:
✫ How to Do Long vs Synthetic Division
----------------------------------------------------
OTHER NOTES:
➤These carefully thought-out lesson is unique because it first reviews the FOUNDATION:
- 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.
➤ 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 or Synthetic Division as part of our skillset.
➤ The entire purpose of Long or Synthetic division is to convert from standard form to factored form so that we can finally solve for the roots!
➤ The lessons tie together WHY students would care about Synthetic Division (and Long Division); which is because it is one of the steps in Rational Roots Theorem in order to ultimately solve for the roots/zeros of a polynomial equation. This is just one of many important connections included in this lesson that students often miss because the information is not compartmentalized in the way that it needs to be so that they can see the big picture.
➤ There is an important example where students can use synthetic division to divide (x^3 - 64) by (x-4) to convert the degree=3 polynomial into factored form... and students will see that they can use the Difference of Perfect Cubes formula to confirm that this works!
➤ 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.
INCLUDED:
- 4 Full Lessons [68 Slides] - PDF & SmartBoard Versions
- 2 Detailed Reference Sheets
- 5 Worksheets
