In my last post, I showed you a procedure for how to factor a quadratic when the leading coefficient is not equal to 1. Here I refine that method slightly with a short cut that makes your work even quicker. However, this method is a bit more difficult—if you are not really good at mental calculations, you will need to practice this a few times to get it down. To compare methods, I’ll use the same quadratic we factored in the last post.

Problem: Factor

- Our first step is the same as in the previous method—we need to find two numbers that multiply together to give (that’s ) and add together to give . Of course, those numbers are the same as they were in the last post: and .

…… - Now here’s the shortcut. Divide both of these numbers by the leading coefficient, . That gives two fractions:

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….. - Next, simplify the fractions if possible. In our example, we get

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….. - In each fraction, the denominator is the coefficient of the
*x*term in our factor and the numerator is the constant term. So our two factors must be and . See the diagram below: