The Sign Map
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 19 of 63.
There are four sign patterns, and one sign rule covers them all. Look at the sign of c first. If c is positive, the two numbers have the same sign, and the sign of b says which sign it is. For x^2 + 7x + 6 the numbers are +1 and +6. For x^2 - 5x + 6 the numbers are -2 and -3.
If c is negative, the two numbers have opposite signs. Find the pair by its difference, and give the larger number the sign of b. For x^2 + x - 12 the numbers are +4 and -3. For x^2 - x - 12 the numbers are -4 and +3.
Use the signs of b and c to decide the signs of the two numbers. Then check the factor pairs to find the pair whose product is c and whose sum is b.
Challenge
EasyFactor x^2 - 5x - 14. First decide the signs of the two numbers. Then find the pair with product -14 and sum -5.
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