The Largest One
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 7 of 63.
Greatest means greatest. 8x + 20 shares a 2, and 2(4x + 10) is true, but look inside: 4x and 10 still share another 2. The job is not done until nothing shared remains: 8x + 20 = 4(2x + 5).
Pulling a smaller common factor is not wrong, just unfinished. You can rescue it by pulling again, 2(4x + 10) = 2 * 2(2x + 5) = 4(2x + 5), but one clean pull of the greatest factor is faster and leaves nothing to forget.
The test for done: scan the leftovers inside the parenthesis. If any number or letter still divides them all, the factor you pulled was not the greatest. The board will hold you to this: a half-pulled factor is not factored form.
Challenge
EasyFactor 18x + 12 completely.
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