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This an example of factoring a quadratic expression using the Greek Method. During my days in middle school, this was one of the ways for showing how to factor a quadratic expression. Notice that there is a methodology to this technique, and no guess and check work involved. The sad truth is that there are math teachers out there that are not familiar with this method of factoring.
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Factor: 9z2 − 12z + 4
Solution:
Step 1: Multiply 9 and 4, that gives 36.
Step 2: Find two factors 36 that sum to -12.
The two factors are -6 and -6, since -6 - 6 = -12 and -6 * -6 = 36.
Step 3: Use these factors from Step 3 to re-write the middle coefficient:
9z2 − 6z − 6z + 4
Step 4: Group the first two terms and last two terms.
(9z2 − 6z) + (−6z + 4)
Step 5: Factor out 3 from the first set of parenthesis. Factor out -2 from the second set of parenthesis.
3z(3z − 2)− 2(3z − 2)
Step 6: Factor out (3z − 2)
(3z - 2)(3z - 2)
