Advanced Polynomial Operations - Complete Interactive Lesson
Part 1: Adding & Subtracting Polynomials
๐ Adding & Subtracting Polynomials
Part 1 of 7 โ Adding & Subtracting Polynomials
Combine like terms (same variable and exponent).
For subtraction: distribute the negative sign first.
Worked Example
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Concept Check ๐ฏ
Add/Subtract Polynomials ๐งฎ
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Coefficient of x?
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Constant term?
Concept Check ๐
Practice
| # | Operation | Result |
|---|---|---|
| 1 |
Challenge Question ๐
Part 2: Multiplying Polynomials
๐ Multiplying Polynomials
Part 2 of 7 โ Multiplying Polynomials
Use FOIL for binomials or distribute each term.
Part 3: Factoring Review
๐ข Factoring Review
Part 3 of 7 โ Factoring Review
Methods
- GCF: Factor out the greatest common factor
- Trinomial: where ,
Part 4: Polynomial Division
๐ Polynomial Division
Part 4 of 7 โ Polynomial Division
Long division or synthetic division (for divisor ).
Part 5: Remainder Theorem
๐งฎ Remainder Theorem
Part 5 of 7 โ Remainder Theorem
When dividing by , the remainder equals .
If , then is a of .
Part 6: Problem-Solving Workshop
๐ ๏ธ Problem-Solving Workshop
Part 6 of 7 โ Problem-Solving Workshop
Solve polynomial problems:
- Model with polynomial expressions
- Factor to find zeros
- Use the remainder theorem to test factors
Worked Example
Rectangle: length , width . Area?
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Part 7: Review & Applications
๐ Review & Applications
Part 7 of 7 โ Review & Applications
Key Concepts
- Add/subtract: combine like terms
- Multiply: FOIL or distribute
- Factor: GCF, trinomial, difference of squares
- Divide: long or synthetic division
- Remainder theorem: = remainder when
Worked Example
Zeros: โ