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? Expand it and compare. 2x + 10 factors as 2(x + 5). Expanding 2(x + 5) gives 2x + 10 again, the expression you started with. The terms and the signs all match.
For example, 2(x + 10) expands to 2x + 20, so it is not a correct factoring of 2x + 10. Multiplying the factors back together shows whether they give the original expression.
To check a factoring, multiply the factors back together. Compare the result with the original expression. Every coefficient and the constant term must match.
Challenge
EasyFactor 6x + 15. Then check your answer by expanding it 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