The Check Is Multiplication
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 4 of 63.
How do you know a factoring is right? Multiply it back. 2x + 10 factors as 2(x + 5); expanding gives 2x + 10 again, the exact expression you started with. Same terms, same signs, nothing missing.
The check catches every classic slip. Pull a 2 out of 2x + 10 but write 2(x + 10), and the check expands to 2x + 20: wrong constant, caught immediately. Factoring and expanding are inverse moves, so each one audits the other.
From here on, treat a factoring as unfinished until you have multiplied it back in your head. It takes seconds and it turns a hopeful answer into a certain one, on this page and in every exam after it.
Challenge
EasyFactor 6x + 15, then check it by expanding in your head.
Try it yourself
Factor the expression
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 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