Choosing a Method
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 52 of 63.
Three methods now stand ready. Factor and split, when a pair exists. Root both sides, when there is no middle term. The formula, always. The craft is choosing the cheapest one that works.
Read the equation first. No middle term, like x^2 = 64: root method, one move. A visible pair, like x^2 + 5x + 4 = 0 (pair 1 and 4): factor and split, two moves. An awkward middle, like x^2 + 3x + 1 = 0: straight to the formula, no time wasted hunting.
A quick discriminant check settles the borderline cases: a perfect square means a pair exists and factoring will be pleasant; anything else means formula. Thirty seconds of reading saves minutes of the wrong method.
Challenge
MediumSolve x^2 - 8x + 15 = 0 by whichever method reads cheapest. Every chip is on.
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: Signs7The Zero Product Rule
A Product That Makes ZeroOne Factor Is EnoughThe Bare XEvery Factor Gets a TurnRecap: Zero Product10The Quadratic Formula
The Formula, StatedThe Number Under the RootSplit the Plus-MinusIt Always WorksChoosing a MethodRecap: The Formula2The 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