Tuesday, November 1, 2011

Solve by Factoring in Elementary Algebra

Learning how to solve equations is one of our main goals in Algebra. At this point, we know how to solve linear equations,

And now we begin to learn how to solve quadratic equations,

One way to solve quadratic equations is to use factoring and the zero-product property. The zero-product property sounds fancy but it simply states that,

So if we can factor a quadratic equation in standard form, equal to zero, we can then set each factor equal to zero and solve the resulting linear equations. For example, solve the following quadratic equation:

Step 1: Express the quadratic equation in standard form, equal to zero.

Step 2: Factor the quadratic expression.

Step 3: Apply the zero-product property and set each variable factor equal to zero.

Step 4: Solve the resulting linear equations.

The solutions are -5, and -3/2. You can check that these are solutions by substituting them into the original equation and verify that they lead to a true statement.  Here is another example on video:

Hopefully you can see that the factoring step is very important in this process. Take care to factor your quadratic equations carefully because this is the step where most students make an error.