Final: Arrange First
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 60 of 63.
The zero product rule only works when a product equals zero. If the equation has a number on the right side, first move every term to the left side so that the right side is zero. Then factor the left side and set each factor equal to zero.
For example, x^2 + 2x = 24 becomes x^2 + 2x - 24 = 0 after you subtract 24 from both sides. The left side factors as (x + 6)(x - 4), so x = -6 or x = 4. Read the signs of the rearranged equation, not the original one, because moving the 24 changed the constant.
Challenge
MediumSolve x^2 - 3x = 28.
Try it yourself
Solve for x
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 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 Completely9The Square Root Method
Undoing a SquareArrange, Then RootA Squared PackageRoots That Are Not WholeRecap: Square Roots12Final Challenges
Final: The Full SweepFinal: Factor and SplitFinal: Arrange FirstFinal: The Rug, ModeledFinal: The Rug, SolvedFinal: No Training Wheels