Longer Hunts
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 14 of 63.
When the constant is bigger, there are more factor pairs to check, but the method is the same. To factor x^2 + 11x + 18, list the pairs of numbers that multiply to 18: 1 and 18, 2 and 9, 3 and 6. Their sums are 19, 11 and 9. You need the pair that adds to 11, so the answer is (x + 2)(x + 9).
Check the pairs in order, starting from 1, so you do not skip one. You can stop as soon as a pair adds to the right number. Only one pair of positive numbers can work, because as the first factor gets bigger, the sum keeps changing in the same direction.
If you have checked every factor pair and none adds to the middle coefficient, the trinomial cannot be factored with whole numbers.
Challenge
EasyFactor x^2 + 13x + 36. List the factor pairs of 36 in order and find the pair that adds to 13.
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