# Factoring Quadratics – Loh Method

## 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.

### Factoring Background

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

Below shows how I made sense of out his method, in simpler terms with visuals. These are images from a Jamboard. Here is a link to a FB Reel presentation and a YouTube 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.