The GCF Route
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 40 of 63.
Not every quadratic equation carries a constant. x^2 + 3x = 0: no pair to hunt, but the GCF from chapter two is right there: x(x + 3) = 0. Split: x = 0 or x = -3.
Every equation of this shape has x = 0 among its solutions, because the bare x is always a factor. The Bare X lesson’s warning about losing the zero applies double here, since this is where those equations come from.
And the tempting wrong move returns: dividing both sides by x. It looks like it simplifies to x + 3 = 0, but it silently assumed x is not zero and threw a solution away. Factor; never divide by the unknown.
Challenge
MediumSolve x^2 - 11x = 0.
Try it yourself
Solve for x
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 Shapes8Solving by Factoring
Factor, Then SplitSigns Under PressureArrange It FirstThe GCF RouteBigger FrontsRecap: Solve by Factoring3The Sum-Product Machine
Reading the ProductHunting the PairThe Machine in LettersLonger HuntsRecap: The Machine6Factor Completely
Two LayersSquares InsideCompletely Means CompletelyThe Deep CheckRecap: Factor Completely