# How do we factor quadratic equations?

##### 2 Answers

A quadratic expression is completely factorizable if and only if its discriminant is positive. Given a quadratic expression of the form

If the discriminant is negative, the solving formula

If the discriminant equals zero, the solving formula reduces to

If the discriminant is positive the same formulas hold, and this time

A quadratic equation is simply another way of solving a problem if the solution cannot be factored logically.

First we can start with some quick review:

Let’s say we have the equation

To begin, we can state the factors of the first term,

Now we can check and see if any of the factors can combine in order to get a

From our factors we can use a -1 and a 3 to get +2. Therefore,

**However** , when the logical factorization seen above is not possible, we can plug our numbers into the *quadratic equation* .

After our a, b, and c values are found we can plug them into the actual quadratic equation.

*Note* : This equation may look intimidating, but as long as you follow factoring rules, you should have no problem. It’s totally normal to come out with an answer containing square roots.