Week 6 — Polynomials & Factoring

Welcome to your Week 6 Start Here page.

Why this matters

Multiplying and factoring polynomials is how a landscaping crew turns a garden bed with a border into one area formula and how a packaging designer finds the volume of a box folded from a flat sheet. Build an expression, take it apart, and check every step yourself.

In plain language

This week is about expressions with several pieces, like the area of a garden bed that has grown in two directions. You will learn to build these expressions by multiplying, and you will learn to take them apart again. Taking an expression apart into pieces that multiply is called factoring (rewriting a sum as a product, the way 12 can be rewritten as 3 times 4). Every answer this week has a built-in check: multiply your pieces back together and see whether you get what you started with.

• Already covered: Week 1 gave you the exponent rules and the distributive property; Week 2 solved equations; Week 3 evaluated functions; Weeks 4 and 5 worked with lines and systems of lines.
• This week: polynomials as objects — their vocabulary, how to add, subtract, and multiply them, and how to factor them.
• How they connect: multiplying polynomials is the distributive property used many times, and every exponent you combine follows the Week 1 product rule.
• Where we're going next: Week 7, Quadratic Equations, uses this week's factoring to solve equations such as x² − 6x + 5 = 0, which begins a new unit on curves.

Focus

How do you build a polynomial by multiplying, take it apart by factoring, and prove each step by checking?

By the end of this module, you should be able to:

• [ ] add, subtract, and multiply polynomials, keeping every middle term
• [ ] factor out a GCF and factor trinomials, with or without a leading coefficient
• [ ] factor a difference of squares and explain why a sum of squares is prime
• [ ] check any product or factoring by expanding it

To-do

Plan your week

1. Read Chapter 6 (about 45 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Model/Build Studio (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: factor x² − 5x − 14 and 2x² + 7x + 3, and expand each answer to check it.

You've got this

Take it in order, and ask your instructor if a step snags.

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