Dr. Po-Shen Loh shared a possible new method for factoring a quadratic. This post provides a layman’s attempt to share the steps that teachers may find intriguing and possibly useful, especially for complex roots.
Dr. Loh’s Website
Here is a link to a page on his site that provides his explanation.
In the expression below, we know we want binomials with constants that are factors of 12 and sum to 8. The factors could be complex, making this challenging.
A Visual Presentation
The premise of Loh’s method is that in lieu of considering two factors separately, you can focus on the following:
- Average of the two factors which is the coefficient of x (linear coefficient) divided by 2. In the case below, that is 8/2 = 4.
- The common distance of each factor from the average, d. In the case below, the factors are converted into the expressions 4-d and 4+d because both are d units away from 4.
This results in a single unknown, the distance d.
The aforementioned expressions with d replace the factors. Now we have an easy quadratic equation to solve using square root. Once d is determined, the factors of 12 are now known and we are on our way.
This method works for complex| factors. This makes Loh’s method less time intensive than using the Quadratic Formula, and there is no formula to memorize.