If a quadratic equation can be factored, it is written as a product of linear terms. Factoring means finding expressions that can be multiplied together to give the expression on one side of the equation. If you choose to write your mathematical statements, here is a list of acceptable math symbols and operators. Often the easiest method of solving a quadratic equation is factoring. To avoid such uncertainties, we encourage you to rely on our equation calculator. Lastly, the method involves some form of trial and error while finding the right constants. On the other hand, there no sure way of determining whether or not an equation is solvable using the factoring method. Thus, not all quadratics can be solved using the above method. Limitation of factoring as a way to solve quadraticsĪlthough the method is highly efficient, it is only applicable to equations with rational roots.
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The following examples will solidify your understanding of factoring as a solution method to quadratic equations: Learning mathematics is best done with examples. You would want to find two constants h, k such that h+k= 5, and h*k=4.ġ and 4 are such candidates: Thus we can rewrite the expression as Check it out Virtual Nerds patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials. Follow along as this tutorial shows you how to graph a quadratic equation to find the solution. Solving quadratic equations by factoring is one of the most efficient methods for finding the roots (solutions) of a quadratic equation. The following example shows the basics of solving a quadratic through factoring. One of the many ways you can solve a quadratic equation is by graphing it and seeing where it crosses the x-axis. In the latter form, the problem reduces to finding or solving linear equations, which are easy to solve. Factoring quadratics is a method that allows us to simplify quadratic expressions and solve equations.
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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. 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: The method is dependent on the fact that if a product of two objects equals zero, then either of the objects equals zero. Solving quadratic equation through factorization is one of the classical methods of solving quadratics. The factoring quadratic solver lets you factor and solve equations of the form ax^2+ bx + c = 0, where a \ne 0.