Every Factor Gets a Turn
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 35 of 63.
The zero product rule works for any number of factors. The equation x(x - 3)(x + 4) = 0 has three factors. Split it into three cases: x = 0, x - 3 = 0 and x + 4 = 0. The three solutions are 0, 3 and -4.
A product of three factors is zero when at least one of the factors is zero. Set each factor equal to zero and solve each case. Include every different solution you find.
Equations like this come from factoring a cubic, as in chapter six. First factor out the common x, then factor the trinomial that is left. The result is a product of three factors, and you split it into three cases. The number of cases matches the number of factors, and each case gives one solution.
Challenge
EasySolve x(x + 1)(x - 6) = 0. There are three factors, so there are three cases.
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: Signs7The Zero Product Rule
A Product That Makes ZeroOne Factor Is EnoughThe Bare XEvery Factor Gets a TurnRecap: Zero Product2The 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 Completely