A Product That Makes Zero
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 32 of 63.
Here is why this section exists. If two numbers multiply to zero, one of them IS zero: there is no other way. 5 * 3 is not zero, 0.1 * 0.1 is not zero; the only products that vanish are the ones holding a zero factor.
Now read (x - 2)(x + 5) = 0. The left side is a product, the right side is zero, so one factor must be zero: either x - 2 = 0 or x + 5 = 0. Two tiny equations, solved on sight: x = 2 or x = -5.
That is the zero product rule, and it is the payoff of every factoring chapter behind you: an equation whose side is factored falls apart into pieces a first-week student could finish. On the board, tap the equation and split it.
Challenge
EasySolve (x + 3)(x - 7) = 0 by splitting the product.
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