Description
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!
Remainder/Factor Theorems: Students are asked to determine whether the binomial is a factor of the dividend (only when the remainder=0); and if it is, then students can convert the polynomial into factored form by multiplying the divisor and quotient together.
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ā« THIS ZIP-FILE IS ALSO INCLUDED IN MY BUNDLES:
1) Entire Polynomials Unit Bundle
2) Long & Synthetic Division and Rational Roots Theorem
ā« CHECK OUT My Related Lessons: Long Division and Rational Root Theorem!
Related Blogs:
ā« Polynomial Long & Synthetic Division
ā« How to Teach Long/Synthetic Division
Related YouTube Video:
ā« How to Do Long vs Synthetic Division
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This lesson [17 slides] is unique because it also ties 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!
INCLUDED:
A TOTAL OF 29 PAGES!
- Full Lesson (PDF & SmartBoard versions) - 17 slides
- Reference sheets: Long division, synthetic division, vocabulary words, rational roots theorem
- Homework worksheet
- Step-by-step answer keys and scaffolded notes to EVERYTHING
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 / Zeros Theorem and Factor & Remainder Theorems [Continued]
Synthetic Division Polynomials | Lesson, Worksheet, Reference Sheets, Keys
Highlights
Save even more with bundles
Description
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!
Remainder/Factor Theorems: Students are asked to determine whether the binomial is a factor of the dividend (only when the remainder=0); and if it is, then students can convert the polynomial into factored form by multiplying the divisor and quotient together.
----------------------------------------------------------------------
ā« THIS ZIP-FILE IS ALSO INCLUDED IN MY BUNDLES:
1) Entire Polynomials Unit Bundle
2) Long & Synthetic Division and Rational Roots Theorem
ā« CHECK OUT My Related Lessons: Long Division and Rational Root Theorem!
Related Blogs:
ā« Polynomial Long & Synthetic Division
ā« How to Teach Long/Synthetic Division
Related YouTube Video:
ā« How to Do Long vs Synthetic Division
----------------------------------------------------------------------
This lesson [17 slides] is unique because it also ties 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!
INCLUDED:
A TOTAL OF 29 PAGES!
- Full Lesson (PDF & SmartBoard versions) - 17 slides
- Reference sheets: Long division, synthetic division, vocabulary words, rational roots theorem
- Homework worksheet
- Step-by-step answer keys and scaffolded notes to EVERYTHING
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 / Zeros Theorem and Factor & Remainder Theorems [Continued]
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