Completely Means Completely
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 29 of 63.
The word completely has teeth. 4x^2 - 16: a student splits it as (2x + 4)(2x - 4) and stops, but look inside each parenthesis: 2x + 4 shares a 2, and so does 2x - 4. Factors of factors count too.
Pulling both 2s gives 4(x + 2)(x - 2), the same result the standing order produces in one clean line: GCF 4 first, then the difference of squares. Layers taken in order never leave crumbs inside.
The finished test, once and for all: no term-shared factor anywhere, no machine pair anywhere, no special shape anywhere, INCLUDING inside every parenthesis. Then and only then is the factoring complete.
Challenge
MediumFactor x^3 - 3x^2 - 28x completely.
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