Factor, Then Split
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 37 of 63.
To solve x^2 + 5x + 6 = 0, factor the left side first. The numbers 2 and 3 add to 5 and multiply to 6, so the equation becomes (x + 2)(x + 3) = 0. Now set each factor equal to zero: x = -2 or x = -3.
To solve by factoring, write the equation with zero on one side. Factor the other side. Then set each factor equal to zero, solve each small equation, and include every different solution.
To check, substitute each answer into the original equation. At x = -2, you get 4 - 10 + 6 = 0. At x = -3, you get 9 - 15 + 6 = 0. Both are true, so both answers are solutions. Factoring did not only 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