Factor, Then Split
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 37 of 63.
Now the two halves of this section meet. x^2 + 5x + 6 = 0 is not factored, but you know the machine: pair 2 and 3, so the equation IS (x + 2)(x + 3) = 0. And a factored equation splits: x = -2 or x = -3.
That is the whole method, and it is the standard one: factor, then split. Every quadratic equation whose trinomial the machine can factor is two moves from solved.
Substitute both answers back into the original if you want the glow of certainty: 4 - 10 + 6 = 0 and 9 - 15 + 6 = 0. Both true. Factoring did not just rewrite the equation; it solved it.
Challenge
MediumSolve x^2 + 9x + 18 = 0 by factoring.
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