Three Terms Share Too
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 9 of 63.
The greatest common factor must divide every term, including the third. In 4x^2 + 8x + 12, the coefficients 4, 8 and 12 have GCF 4. The constant term 12 has no factor of x, so no x is taken out. The result is 4(x^2 + 2x + 3).
Dividing each term by 4 leaves x^2 + 2x + 3 inside the parentheses. Check by expanding 4(x^2 + 2x + 3) term by term.
Sometimes the trinomial inside can be factored further, using methods you will learn in the next chapter. Sometimes it cannot. Here x^2 + 2x + 3 cannot be factored further. When the inside cannot be factored any more, the whole factoring is finished.
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