Week 6 · Readings & resources

Week 6 — Readings & Resources

College Algebra Free sample edition

Your primary reading is Chapter 6 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 11 items (5 readings and 6 videos). Allow 73–89 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (19–22 min total)

① What are the parts, and where does the middle term come from? Building polynomials

Chapter 6, Section “Multiply with FOIL and check at a value” · Session 1, Segment 2, “Adding, subtracting, and multiplying polynomials” · Remember: two binomials make four products, and the square of a binomial always keeps its middle term.

Tutorial 6: Polynomials — Virtual Math Lab — a step-by-step tutorial that names the parts of a polynomial (terms, coefficients, and the constant term), sorts monomials, binomials, and trinomials, and finds the degree and the leading coefficient; read through the section on degree, since the later sections on adding and multiplying repeat the other items here. Use it while working through the Week-6 module overview. (reading, 8–12 min)
How to Multiply Binomials: FOIL Method and Special Cases Explained — XO Math — a short walkthrough of first, outer, inner, last on several pairs of binomials, then the special cases where a pattern saves time. (video, 5 min) (captions: creator)
Special Binomial Products — Math is Fun — the three special products with an area picture for each one, and a clear warning not to drop the middle term when you square a sum. (reading, 5–8 min)
Special Binomial Products — turksvids — worked examples of squaring a sum, squaring a difference, and multiplying a sum by a difference, done by pattern and checked. (video, 5 min) (captions: automatic)

② Which two numbers? The GCF and trinomials

Chapter 6, Section “Factor trinomials that start with x squared” · Session 2, Segment 4, “The greatest common factor and trinomials” · Remember: pull out the greatest common factor first, then look for two numbers whose product is c and whose sum is b.

Factoring a Binomial and Trinomial with a Common Factor — Mathispower4u — two short examples of finding the greatest common factor and pulling it out before anything else. (video, 4 min) (captions: creator)
Factoring a Trinomial with Leading Coefficient of 1 - The Basics — Mathispower4u — the product-and-sum hunt worked through every sign combination, with each answer checked by multiplying back out. (video, 11 min) (captions: creator)
Factoring Simple Quadratics — Purplemath — a step-by-step page on finding factors of c that add to b, with sign rules that tell you in advance whether the two numbers are positive or negative. Stop here before solving equations by factoring; next week takes that up. (reading, 8–12 min)
Factoring Trinomials ax2+bx+c By Grouping — The Organic Chemistry Tutor — many examples in a row of the ac method: multiply a and c, split the middle term, and group; watch the first few examples and stop when you feel confident. (video, 15 min) (captions: automatic)

③ Does it factor at all? Differences and sums of squares

Chapter 6, Section “Spot a difference of squares, and leave a sum of squares alone” · Session 2, Segment 6, “Squares and grouping” · Remember: a difference of squares always factors as a sum times a difference, but a sum of squares is prime over the real numbers.

Factoring the Difference of Two Squares - Ex 1 — Patrick J — one short, complete example of spotting two perfect squares with a minus between them and writing the two factors. (video, 3 min) (captions: automatic)
Factoring a Difference of Two Squares — Virtual Math Lab — a short section of a factoring tutorial that writes a difference of two squares as a sum times a difference, works two examples after first checking for a common factor, and states plainly that a sum of two squares does not factor. (reading, 6–9 min)

Optional one-stop reference (free online reference)

Polynomial — Wolfram MathWorld — a mathematics encyclopedia's entry on polynomials; read the opening definition as a sum of powers times coefficients and its note that the highest power is the degree, and skip everything after it, which goes far beyond this course. (reading, 3–5 min)

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.

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