The Minus Version
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 24 of 63.
A perfect square can hide behind a minus. x^2 - 10x + 25: half of -10 is -5, and (-5)^2 = 25. The signature holds with the minus riding along, and the square is (x - 5)^2.
The constant stays POSITIVE either way, because squaring kills the sign; only the middle betrays which version you have. Minus middle, minus inside the square: (a - b)^2 = a^2 - 2ab + b^2.
Keep the two special shapes apart by their middles: no middle at all is the difference of squares; a middle equal to twice the root of the constant is the perfect square, plus or minus telling you which sign lives inside.
Challenge
EasyFactor x^2 - 12x + 36.
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