The Reverse Gear
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 2 of 63.
Your first factoring. 3x + 12: both terms are divisible by 3, so 3 can be pulled out front, leaving what remains inside a parenthesis: 3x + 12 = 3(x + 4).
What remains is found by dividing each term by the factor you pulled: 3x / 3 = x and 12 / 3 = 4. The distributive property run in reverse: instead of pushing the 3 in, you pull it out.
Every factoring in this section works this way: find something every term shares, pull it out front, keep the leftovers inside. The only skill is spotting what is shared, and the chapters ahead train that eye on bigger and bigger shapes.
Challenge
EasyFactor 4x + 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