R.4 Polynomials

Miller & Gerken, College Algebra 2e — Pages 44-55

Learning Objectives

  • Identify polynomial degree, leading coefficient, and constant term

  • Add and subtract polynomials

  • Multiply polynomials

  • Apply special product formulas

Key Concepts

Polynomial Terminology

Polynomial in \(x\)

\(a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0\)

Degree

The highest power of the variable

Leading Coefficient

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

  1. Key point 1

  2. Key point 2

  3. Key point 3

Study Notes

Personal observations and things to remember…​