Factoring to Solve Equations

Factoring is one method used to solve quadratic (second-degree) equations.  A quadratic (or second-degree) equation is an equation in which the variable has an exponent of 2.  First the equation must be written in standard form .  This means that the polynomial must be in descending form and set equal to zero.  Next, you must factor the polynomial.  Once the polynomial is factored, set any factor which contains a variable equal to zero and solve (using isolation) for the variable.  This works because of the zero factor theorem which states that if the product of two numbers is zero then either one or both of the factors must equal zero.  Once you have found the value for the variable which would make the factor equal zero, you should check your answer in the original equation.  Every quadratic equation has two solutions, although in the case of a perfect square trinomial both of the solutions are the same.

If the equation is factored and set equal to zero as in the example, , then  and

Solve the equation, .  First, you must get the equation in standard form.  This means that you must add 16 to both sides so that the  –16 is removed from the left side of the equation and the equation will then be equal to zero …  … .  Now you are ready to factor, .  Set the factors equal to zero.  Since is repeated twice as a factor, there are two solutions, but they are both the same.  Thus, is the only “unique” solution to this problem.  This is a perfect square trinomial, which factored into the square of a binomial.

If the problem has a degree of three (in other words the variable in the equation is cubed) then you will find three solutions.  Example:  .
First, factor the GCF of  +2x  from each of the terms of the polynomial … .
Next factor, .  We now have three factors which contain variables, therefore,  and  and .  This example of a third degree equation has three solutions .

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 15-Nov-2007