Two Layers
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 27 of 63.
Real factoring problems come in layers. 2x^2 + 10x + 12: the machine wants a leading x^2, but a GCF of 2 is in the way. Pull it first: 2(x^2 + 5x + 6). NOW the machine reads the inside: 2(x + 2)(x + 3).
GCF first is the standing order. It clears the ground for every other tool, shrinks the numbers you hunt through, and its skipping is the single most common reason a factorable expression looks impossible.
Factored completely means every layer is done: nothing shared among the terms, nothing left for the machine, nothing left for the special shapes. The board grades against that standard, exactly as your exams will.
Challenge
MediumFactor 2x^3 + 6x^2 + 4x completely: two layers.
Try it yourself
Factor the expression
Test yourselfThis 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 GearUn-Distributing LettersThe Check Is MultiplicationRecap: First Factors4Minus Signs in the Machine
A Negative ProductWhich One Gets the MinusBoth NegativeThe Sign MapRecap: Signs2The Greatest Common Factor
Number and Letter TogetherThe Largest OneHigher PowersThree Terms Share TooRecap: The GCF5Special Shapes
A Missing MiddleThe Shape in LettersThe Perfect SquareThe Minus VersionPrime PolynomialsRecap: Special Shapes3The Sum-Product Machine
Reading the ProductHunting the PairThe Machine in LettersLonger HuntsRecap: The Machine6Factor Completely
Two LayersSquares InsideCompletely Means CompletelyThe Deep CheckRecap: Factor Completely