Signs Under Pressure
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 38 of 63.
The sign map from chapter four earns its keep inside equations. x^2 - x - 12 = 0: negative constant, so opposite signs; the pair differing by 1 is 4 and 3, minus on the larger: (x - 4)(x + 3) = 0.
Split: x = 4 or x = -3. Note the double flip a solver's eye must survive: the pair was -4 and +3 inside the parentheses, and the SOLUTIONS flip those signs again to 4 and -3.
Keep the two layers separate in your head: the sign map chooses the pair, the little equations flip them. Rushing the two layers into one guess is where wrong signs are born.
Challenge
MediumSolve x^2 - 4x - 21 = 0. Map first, split second.
Try it yourself
Solve for x
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 Shapes8Solving by Factoring
Factor, Then SplitSigns Under PressureArrange It FirstThe GCF RouteBigger FrontsRecap: Solve by Factoring3The Sum-Product Machine
Reading the ProductHunting the PairThe Machine in LettersLonger HuntsRecap: The Machine6Factor Completely
Two LayersSquares InsideCompletely Means CompletelyThe Deep CheckRecap: Factor Completely