For the first time in this course, you’ll learn how to convert a quadratic that’s in its **general form** to a quadratic in **factored form**.

General form: y = **a**x² + **b**x + **c **→ Factored form: y = **a**(x –** r**)(x – **s**) *where r and s represent the x coordinates of the roots.*

The first technique you can try is **trial-and-error**.

Take, for example, the quadratic equation:

x² – x – 6 = 0

First, identify the** c** constant and **b** coefficients. The **c** constant is -6, the **b** coefficient it -1. You have to do this all the time.

Next, you need to find two factors of **-6** that multiply to it, and those same two factors add to **-1**.

The only possibility that words is -3 and +2.

-3 × (+2) = **-6**

-3 + 2 = **-1**

You then rewrite your equation as two factors: y = (x **– 6**)(x – **1**).

Pointers to keep in mind:

Alwaysbegin the process of factoring a quadratic by common factoring if possible. In the example shown above, nothing could be common factored.- This technique can only be tried if the
acoefficient is 1. Otherwise, another technique known as factoring by decomposition is used (next lesson).- Many quadratic expressions, such as x² + 3x + 5, cannot be factored over the integers. No two integers have a product of 5 and a sum of 3. In that case, we’ll use the
quadratic formula(more to come on this later on).

Now let’s see this in action.