R.4 Polynomials
Miller & Gerken, College Algebra 2e — Pages 44-55
Learning Objectives
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Identify polynomial degree, leading coefficient, and constant term
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Add and subtract polynomials
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Multiply polynomials
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Apply special product formulas
Key Concepts
Polynomial Terminology
- Polynomial in \(x\)
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\(a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0\)
- Degree
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The highest power of the variable
- Leading Coefficient
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The coefficient of the highest degree term
Special Products
| Pattern | Formula |
|---|---|
Difference of Squares |
\((a+b)(a-b) = a^2 - b^2\) |
Square of a Sum |
\((a+b)^2 = a^2 + 2ab + b^2\) |
Square of a Difference |
\((a-b)^2 = a^2 - 2ab + b^2\) |
Cube of a Sum |
\((a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) |
Cube of a Difference |
\((a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3\) |
Examples
Example 1. Example 1 (p. XX)
Work through textbook example…
Practice Problems
Problem 1 (p. XX, #YY)
Problem:
My Work:
Answer:
Section Summary
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Key point 1
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Key point 2
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Key point 3