Three Terms Share Too
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 9 of 63.
The GCF does not care how many terms there are; it only asks what ALL of them share. 4x^2 + 8x + 12: the numbers 4, 8 and 12 all divide by 4, and no letter is in every term (the 12 has no x). So the pull is the number alone: 4(x^2 + 2x + 3).
Each of the three terms is divided by 4 on the way in: x^2, 2x, 3. A three-term check is three little expansions, and the habit from chapter one still pays: multiply back, term by term.
Sometimes the trinomial inside can be factored further by tools you will meet in the next chapter, and sometimes it cannot. Here x^2 + 2x + 3 keeps its shape; when the inside is done, the whole factoring is done.
Challenge
EasyFactor 5x^2 + 10x + 20.
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