Unit 7 — Polynomials

Unit 7 · Polynomials

Polynomials

Classify, add, subtract, multiply, and factor polynomials. Master special products and factoring techniques that are essential for all higher-level algebra.

Estimated Time

35–45 minutes

Difficulty

Intermediate

7 Lessons
6 Learning Goals
10 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 7 — Polynomials is where algebra gets expressive. You will classify, add, subtract, multiply, and factor polynomial expressions — including special products and trinomial factoring techniques that are essential for solving quadratic equations in Unit 8.

Learning Objectives

By the end of this unit, you will be able to:

Goal 1Identify, classify, and write polynomials in standard form.
Goal 2Add and subtract polynomials by combining like terms.
Goal 3Multiply polynomials using the distributive property and FOIL method.
Goal 4Apply special product patterns: perfect square trinomials and difference of squares.
Goal 5Factor polynomials by extracting the greatest common factor (GCF).
Goal 6Factor trinomials of the form ax² + bx + c using grouping and the AC method.

Skills You Will Master

Classifying polynomials
Adding & subtracting
Multiplying & FOIL
Special products
Factoring with GCF
Factoring trinomials

Real-World Connection

Polynomials are the building blocks of advanced mathematics and appear throughout science, engineering, and technology. Engineers use polynomial equations to model the trajectory of a projectile. Economists use them to model cost and revenue curves. Computer graphics rely on polynomial curves (called splines) to render smooth shapes in video games and animated films. Even the formula for compound interest is a polynomial. Learning to manipulate and factor polynomials gives you the algebraic fluency needed for every math course that follows.

Chapter Checklist

Recommended steps for completing each chapter

  • Read the Workbook
  • Complete the Independent Study
  • Finish the Exit Ticket
  • Take the Quiz
  • Review the Answer Key
  • Continue to the Next Chapter