Number and Letter Together
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 6 of 63.
Most terms share more than one thing. 6x^2 + 9x: the numbers 6 and 9 share a 3, and both terms carry an x. Pull out both at once, as the single factor 3x: 6x^2 + 9x = 3x(2x + 3).
The leftovers come from dividing each term by the whole 3x: 6x^2 / (3x) = 2x and 9x / (3x) = 3. Numbers divide, exponents subtract, exactly the two-track habit from last section.
The factor you pull, number part and letter part together, is called the greatest common factor, the GCF. Greatest because you take all of what is shared: every common number and every common letter, in one pull.
Challenge
EasyFactor 10x^2 + 4x by 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