Factoring Quadratic Equations

Factoring quadratic equations is another way of solving quadratic equations. However, not every quadratic equation can be factored easily. Factoring quadratic equations is often only done when you can see obvious factors of the quadratic equations. Usually, factoring quadratic equations gets easier with practice and familiarity with quadratic functions.

Solving quadratic equations by factoring

Sometimes, it is faster to solve quadratic equations by factoring. Graphing quadratic equations may take too long when you can see the obvious factors and solutions of the quadratic equations. Let's use the example we used in the previous section to illustrate how factoring quadratic equations are done in algebra.

Examples of factoring quadratic equations

Suppose we need to solve the same quadratic equations as we did with the method of Graphing Quadratic Equations. In factoring quadratic equations, we replace one of the unknowns in the quadratic equation. Let's replace y to give:

We now have one quadratic equation in one variable, x. We now need to find the values or roots of x which satisfy the quadratic equation. By factoring the quadratic equation, we have:

By factoring the quadratic equations, we now have the values of x and can then substitute for the values of y. We will discuss factorization in another section.