Amazingly easy way to factor quadratics when A ≠ 1

24 Jul

Towards the end of the school year, two of my previous 7th grade students who were now graduating 8th graders visited me after school. Besides informing me in whispers on the current 8th grade gossip, they shared how their classmate who is from Vietnam factors quadratics when A ≠ 1. I had this student last year, and it was quite fascinating how he approached problems, usually graphically and in this case, just differently.

So lets say you have the quadratic: 6x² + 13x -5  and you want to factor it.  Some teachers have the students go through a trial and error process using the factors of A (6) and the the factors of C (-5).  Tedious but doable.

Here’s how this student did it:

Ax² + Bx + C

6x² + 13x -5    Quadratic to factor

1.  Find two numbers that have a product of AC (6 x -5 = -30) and a sum of B (13)  —  like how we factor when A = 1

Okay,  15 and -2 satisfy this criteria.

2. Next, create two ratios using 15 and -2 as the numerators, and A (6) the denominator in both cases.

15/6   and -2/6   now simplify these ratios to 5/2 and -1/3

3. Now take these ratios and create the factor  (2x + 5) from 5/2   and (3x -1) from -1/3

Factored quadratic is (2x+5)(3x-1).

Cool, right? Works for all quadratics that can be factored.  Explaining why it works will have to be another post (or perhaps a comment will explain) 🙂

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