Completely Means Completely
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 29 of 63.
Factored completely means that no factor can be factored any further. Take 4x^2 - 16. You might write (2x + 4)(2x - 4) and stop. But look inside each parenthesis. 2x + 4 has a common factor of 2, and so does 2x - 4. A factor can have factors of its own.
Factor the 2 out of each parenthesis to get 4(x + 2)(x - 2). You can also factor out the GCF 4 first, then use the difference of squares rule on x^2 - 4. Both ways give the same answer.
To factor completely over the integers, look at every factor you get. Take out any common factor that is left. Factor any trinomial that can be factored. Check for a difference of squares or a perfect square trinomial. Stop only when no factor can be factored any further.
Challenge
MediumFactor x^3 - 3x^2 - 28x 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