Number and Letter Together
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 6 of 63.
Often the terms share more than one thing. In 6x^2 + 9x, the numbers 6 and 9 share a factor of 3, and both terms contain an x. Take out both at once, as the single factor 3x: 6x^2 + 9x = 3x(2x + 3).
To check, multiply 3x by each term inside: 3x × 2x = 6x^2 and 3x × 3 = 9x. Both terms of the original expression come back.
The factor you take out, with its number part and its letter part together, is called the greatest common factor, or GCF. It is called greatest because it contains everything the terms share: every common number and every common letter, taken out in one step.
Challenge
EasyFactor 10x^2 + 4x by taking out its GCF.
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