A Negative Product
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 16 of 63.
To factor x^2 + 2x - 8, find two numbers with product -8 and sum 2. A negative product means the two numbers have opposite signs. One number is positive and the other is negative.
List the factor pairs of 8, which are 1 and 8, and 2 and 4. Put a minus sign on one number of each pair and look for the pair that adds to 2. The pair 4 and -2 works, because 4 - 2 = 2. So x^2 + 2x - 8 = (x + 4)(x - 2). The factor x - 2 means x + (-2), written in the usual short way.
For x^2 + bx + c, the two numbers in the factors must multiply to c and add to b. If c is negative, the two numbers have opposite signs. If c is positive, they have the same sign. Then use b to decide which number gets which sign.
Challenge
EasyFactor x^2 + 3x - 10. The constant is negative, so the two numbers have opposite signs. Find the pair with product -10 and sum 3.
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