Algebra 2 – The “Magic Number” Technique to Factoring

If your expression was a number other than 1 in front of the squared term, I call that number “magic” because it is involved in a few magical steps to get an answer.

Suppose you’d like to factor this expression:

Step 1: Factor out the GCF if possible. In this example, there is no GCF. You must factor out a GCF before you continue to step 2.

Step 2: Convert the expression to one where the squared term has a coefficient of 1. Do that by stripping the squared term of its current coefficient, in this case 15 and call that number the “magic number“.

Create another expression that has a squared term, the same middle x term, and the last constant being the magic number multiplied by the original constant. Here is the new expression to deal with:

Step 3:  Factor the new “simplified” expression to get

Step 4: Using the “magic number”, which in this case is 15, make fractions out of the numbers generated in step 3. Here is the expression:

Step 5: Simplify the fractions. This is the result of the simplification:

Step 6: If you still have fractions after simplifying the fractions, move the denominations of those fractions to the front of the variable. Here’s what we get: