Factoring Quadratic Equations

Posted on | December 25, 2011 | No Comments

Factoring Quadratic Equations Calculator

To easily factor a quadratic equation that has at least one rel root, we can use the following factoring calculator:

1. First, enter the quadratic equation you would like to factor.

The Solution Will Appear Here!

The standard view of a quadratic equation is: ±ax²±bx±c=0. Factoring such an equation, means to transform it into this view: ±a(x-x₁)(x-x₂)=0 , where x₁ and x₂ are the roots of the equation. Using this formula, we can easily factor any quadratic equation, for which D >= 0, in more convenient view. As you can see, to convert it into a factored view, obviously we need to solve it and find it’s roots, and then replace them in the formula. Let’s see how this works.

Example: Let’s factor the equation -4x₂+6x+4=0. We can use the standard formulas for solving it and find that it has two roots:
x₁ = -0.5 and x₂ = 2

So using the formula: a(x-x₁)(x-x₂)=0, now we can simply convert the equation into factored view, by replacing x₁ and x₂ with their values:

-4(x-(-0.5))(x-2)=0 => -4(x+0.5)(x-2)=0 – the quadratic equation in factored view.

But why do we need to factor these equations? Well, there are could be many reasons for this. One of them is that an equation in this view can be very easily solved, without using any complicated formulas. In our example we can simply divide the two sides by -4 to get:

(x+0.5)(x-2)=0

This means that x+0.5=0 or x-2=0, or the solutions are:

x+0.5=0 U x-2=0 => x=-0.5 U x=2

If you need to factor polynomials, visit the factoring calculator site, where you will find various free widgets for factorization.

To further explore quadratic functions, you can use our quadratic equation calculator or quadratic formula explorer. Nice and powerfull online tools…