Factoring the general quadratic equation

A method

We want to rewrite the general quadratic equation in the form .

To do this we look for two numbers and such that and .

We can now rewrite the general quadratic equation as …

Now, since then and thus also .

Therefore we can further write the general quadratic equation as …

Let’s try some examples.

Example 1

, and ; and ; so . Therefore …

Example 2

, and ; and ; so . Therefore …

Example 3

, and ; and , so . Therefore …