Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 6 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 5 — Perform operations on polynomials and factor polynomial expressions using the GCF, trinomial factoring, the difference of squares, and factoring by grouping.

This file holds two pieces: (A) the Module 6 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 6 meeting Tue Oct 6 and Thu Oct 8, and end-of-week work due Sunday Oct 11, 11:59 p.m. Module start date is Mon Oct 5 (no holidays this week). Adjust the day-of-week and times to match your section.

(A) Module 6 Overview — Start Here

Welcome to Week 6: Polynomials & Factoring

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

Polynomials are the language of algebra — sums and products of terms you've been meeting since Week 1. This week you'll learn to fluently add, subtract, and multiply them (including the powerful special-product shortcuts), and then reverse that multiplication through factoring. Factoring is the skill that unlocks every quadratic you'll see for the rest of the course.

The week's big question

"If multiplication combines factors into a product, what's the systematic way to go backwards — to pull a polynomial apart into its factors?"

By Sunday you'll expand (a+b)² without missing the middle term 2ab, factor a trinomial by finding the right pair of numbers, recognize a difference of squares on sight, and apply factoring by grouping when a polynomial has four terms.

By the end of this week, you can…

Use this as a checklist. If you can do all four, you're ready for Quiz 6.

• [ ] Add, subtract, and multiply polynomials, including FOIL and the special products (a+b)², (a−b)², and (a+b)(a−b).
• [ ] Factor out the GCF from any polynomial as the first step — always.
• [ ] Factor trinomials of the form x²+bx+c (find two numbers that multiply to c and add to b) and ax²+bx+c (leading-coefficient form).
• [ ] Factor a difference of squares (a²−b²) and recognize that a sum of squares (a²+b²) does not factor over the reals.
• [ ] Factor by grouping when a polynomial has four terms.

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: you'll use a chatbot to draft, and then you judge its work. Chatbots often forget the middle term 2ab when squaring a binomial, or confuse the sign in a factored trinomial. Catching the model is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• The middle term is sacred. The #1 error of the week is (a+b)² = a²+b². It's wrong — the correct expansion is a²+2ab+b². The 2ab comes from FOIL's outer + inner terms; never skip it.
• GCF first, always. Before you try any other factoring strategy, factor out the GCF. It simplifies every subsequent step and catches hidden structure.
• Factoring = reverse multiplication. If you're not sure whether (x+3)(x+4) is right, expand it and check. That check habit is worth more than memorizing a rule.
• Sum of squares is a dead end. x²+16 does NOT factor over the reals. Recognize that pattern and move on rather than searching for factors that don't exist.
• Use Desmos as a factoring check. Graph y = x²+7x+12 and y = (x+3)(x+4) — if they're the same curve, your factoring is correct.

See you Tuesday.

(B) Welcome Announcement — Module 6

Release setting: post on the module's start day (offset = 0 days), i.e., Mon Oct 5, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Mon Oct 5."

Subject: Week 6 — Let's undo multiplication 🔄

Hi everyone,

Quick question: if I told you a rectangle has an area of x²+7x+12 square feet, could you find its length and width?

That's factoring — and it's exactly what we're learning this week. Week 6 is Polynomials & Factoring, and the big idea is this: multiplication and factoring are inverse operations, just like addition and subtraction. Once you can go both directions, you can solve problems that looked unsolvable a week ago (and we'll use that starting in Week 7).

The week's big question: If multiplication builds a product from factors, what's the systematic way to take a product apart?

Two things to watch for this week:

1. (a+b)² ≠ a²+b². This is the most common algebra mistake in the course. The correct expansion is a²+2ab+b², and the middle term 2ab is missing from the wrong version. I'll name this trap on Tuesday and give you a foolproof check.
2. Sum of squares doesn't factor. x²+25 has no real factors — don't go searching for them. We'll be clear on which patterns factor and which don't.

Three things not to miss:

1. Lecture Tutorial 6 — work through polynomial operations and factoring with one approved chatbot and submit the share link. You'll catch a chatbot that forgets the middle term. Due Sun Oct 11.
2. Quiz 6 (no AI on quizzes) and Discussion 6 — "Who's Right about (a+b)²?" also close Sun Oct 11 — the discussion is a quick AI dialogue you summarize and post, so start early and leave time to reply to classmates.
3. Assignment 6 — four AI-coached problems with a self-scored report; due Sun Oct 11.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates. Bring pencil and paper; this week's work is best done by hand first, then checked with technology.

See you Tuesday,
Prof. Calloway