Factoring quadratic solver | Step-by-Step

A Worked example to illustrate how the factoring calculator Works:

The factoring quadratic solver lets you factor and solve equations of the form ax^2+ bx + c = 0, where a \ne 0. Solving quadratic equation through factorization is one of the classical methods of solving quadratics.

The method is dependent on the fact that if a product of two objects equals zero, then either of the objects equals zero. To solve a quadratic through this method, we first factor the equation into a product of two first degree polynomials as given in the following example:

If ax^2+ bx + c = 0, where a ≠ 0 is a factorable quadratic equation, then it can be represented in the form ax^2+ bx + c = (x+h)(x+k)=0, where h, k are constants. In the latter form, the problem reduces to finding or solving linear equations, which are easy to solve.

The following example shows the basics of solving a quadratic through factoring.

Example 1:

Given: x^2+5x+4=0

You would want to find two constants h, k such that h+k= 5, and h*k=4.

1 and 4 are such candidates: Thus we can rewrite the expression as

x^2+5x+4=(x+1)(x+4)=0

and (x+1) =0 OR (x+4)=0

Thus x=-1 Or x=-4

Learning mathematics is best done with examples. The following examples will solidify your understanding of factoring as a solution method to quadratic equations:

Solved Factoring Examples with Steps

Limitation of factoring as a way to solve quadratics

Although the method is highly efficient, it is only applicable to equations with rational roots. Thus, not all quadratics can be solved using the above method. On the other hand, there no sure way of determining whether or not an equation is solvable using the factoring method. Lastly, the method involves some form of trial and error while finding the right constants. To avoid such uncertainties, we encourage you to rely on our equation calculator. It is free and fun to use. Solving algebra never became this easy.