Arrange It First
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 39 of 63.
The zero product rule needs a zero. x^2 = 7x - 10 offers none, so build one: move everything to the left, x^2 - 7x + 10 = 0, and only now factor and split: (x - 2)(x - 5) = 0, so x = 2 or x = 5.
Beware the shortcut that skips the arranging. From (x - 1)(x + 2) = 4 you may NOT conclude a factor is 4: plenty of products make 4 without either factor being it, 2 * 2 for one. The rule is about zero and only zero.
So the full method has three beats: arrange to “something = 0”, factor, split. The first beat is pure Fundamentals, moving terms across the equals sign, and it is the beat exams love to test.
Challenge
MediumSolve x^2 + 4x = 12. Build the zero first.
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