Longer Hunts
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 14 of 63.
Bigger constants mean longer lists, and the walk stays the same. x^2 + 11x + 18: pairs of 18 are 1 * 18, 2 * 9, 3 * 6, with sums 19, 11, 9. The middle wants 11, so the pair is 2 and 9: (x + 2)(x + 9).
Two habits keep long hunts short. Walk the list in order so nothing is skipped, and stop the moment a sum matches: for a given b and c, at most one pair of positive numbers can work, because making one factor bigger always drags the sum in one direction.
And when the list runs out with no match, that is an answer too: the trinomial does not factor over whole numbers. You will meet those, and the machine failing IS the finding.
Challenge
EasyFactor x^2 + 13x + 36. The list for 36 is worth walking in order.
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