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Two Directions

Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 1 of 63.

Last section you multiplied polynomials: 4x(x + 3) expands to 4x^2 + 12x. This section walks the same road the other way. Writing 4x^2 + 12x as 4x(x + 3) is called factoring: turning a sum back into a product.

The two forms are the same value in different clothes. Expanded form shows the terms; factored form shows the ingredients that multiply together. Neither is more correct, but each answers different questions, and the next chapters are about when and how to reach the factored one.

Why bother? One reason above all, coming in chapter seven: an equation whose side is a product can be solved by looking at the factors one at a time. Factoring is the key that unlocks quadratic equations, and this whole section is the making of that key.

Challenge

Easy

Warm up in the familiar direction: expand 5x(x + 2).

Try it yourself

5x(x + 2)

Simplify the expression

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Factoring & Quadratics

1What Factoring Is

Two DirectionsThe Reverse Gear Un-Distributing Letters The Check Is Multiplication Recap: First Factors

4Minus Signs in the Machine

A Negative Product Which One Gets the Minus Both Negative The Sign Map Recap: Signs

7The Zero Product Rule

A Product That Makes Zero One Factor Is Enough The Bare X Every Factor Gets a Turn Recap: Zero Product

10The Quadratic Formula

The Formula, Stated The Number Under the Root Split the Plus-Minus It Always Works Choosing a Method Recap: The Formula

2The Greatest Common Factor

Number and Letter Together The Largest One Higher Powers Three Terms Share Too Recap: The GCF

5Special Shapes

A Missing Middle The Shape in Letters The Perfect Square The Minus Version Prime Polynomials Recap: Special Shapes

8Solving by Factoring

Factor, Then Split Signs Under Pressure Arrange It First The GCF Route Bigger Fronts Recap: Solve by Factoring

11How Many Solutions?

Two, One, or None The Double Root None at All Recap: Counting Solutions

3The Sum-Product Machine

Reading the Product Hunting the Pair The Machine in Letters Longer Hunts Recap: The Machine

6Factor Completely

Two Layers Squares Inside Completely Means Completely The Deep Check Recap: Factor Completely

9The Square Root Method

Undoing a Square Arrange, Then Root A Squared Package Roots That Are Not Whole Recap: Square Roots

12Final Challenges

Final: The Full Sweep Final: Factor and Split Final: Arrange First Final: The Rug, Modeled Final: The Rug, Solved Final: No Training Wheels