Two Layers
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 27 of 63.
To factor 2x^2 + 10x + 12, start with the greatest common factor. Every term is divisible by 2, so factor it out: 2(x^2 + 5x + 6). Now factor the trinomial inside. The pair 2 and 3 has product 6 and sum 5, so the answer is 2(x + 2)(x + 3).
Always factor out the greatest common factor first. It makes the coefficients smaller, and it can show a trinomial or a special pattern that you can factor further.
A polynomial is factored completely when none of its factors can be factored any further over the integers. After you take out the GCF, look at every factor that is left. Check whether another factoring method applies to it.
Challenge
MediumFactor 2x^3 + 6x^2 + 4x completely. It takes two steps.
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