Solving Quadratic Equations by Factoring 06:09 minutes

Video Transcript

Transcript Solving Quadratic Equations by Factoring

Every day in San Francisco, on Pier 39, there is a street performer named FOIL. People pass by him, but no one seems to notice the inconspicuous man. FOIL has a secret. At night, he morphs into a superhero, armed with a sparkling wit and powerful tools: factors, sums, the Zero Factor Property and most importantly, his powerful calculator wrist. What’s that, you ask? Hold on to that thought. The mayor has just made an announcement: his two daughters have been kidnapped by a pair of bad guys and they are holding the girls by the dock but can he save the girls and foil the crime just in time?
FOIL will need his calculator, his super smarts and how to solve quadratic equations by factoring. The girls are locked up in a container secured by a very complicated code. It won’t be easy to crack this code. To figure it out, FOIL must find the solutions for this quadratic equation.

Zero Factor Property

Let’s start by having a look at the Zero Factor Property. In this example, either one or both of the factors have to be zero to get a true statement. It's important that you always set the expression equal to zero, otherwise this rule won’t work. Set each set of parentheses equal to zero. If you use opposite operations, you should get two answers for x, -6 and 1. When you plug either of these two values into the original equation, you should get 0. Remember to always check your solutions.

Reverse FOIL Method

Now that we understand the main concept of the Zero Factor Property, let’s look at the quadratic equation FOIL has to solve. To factor this quadratic equation we can use the reverse foil method. We have to find the values for the variables 'm' and 'n'. In our example, m(n) = -6 and mx + nx = 1x. Therefore, 'm' plus 'n' have to be equal to 1. So now we have to find factors of -6 that sum to 1. As you can see, the product of -2 and 3 is equal to -6 and the sum of -2 and 3 is equal to 1. Perfect, we found the values for 'm' and 'n', so we can subtitute the variable 'm' and 'n' in the reverse FOIL method with these values.
So we factored our quadratic equation into two binomials (x-2) and (x+3). As always, it’s a good idea to check your work by FOILing. Good job, the factorization is proved. But, FOIL's work is not done. Although he's figured out the factors, he doesn't have a solution. To calculate the solution and free the girls, he must use the Zero Factor Property. He sets each binomial factor to zero and solves for 'x' in each case. By using opposite operations, he gets two answers for 'x', -3 and 2.

Let’s try some more problems and investigate some strategies to make these calculations easier to work with. For this first problem, modify the equation to write it in standard form to set the equation equal to zero. Now use the reverse of FOIL to factor, and then apply the Zero Factor Property to find the solutions for the variable. For this equation there is just one solution, x equals 2. I know you're anxious to find out what’s happening on the dock, but be patient.
Let’s work out one last example. This problem looks different because it has no constant. To solve, you can factor out the greatest common factor, which is 'x'. The first solution for 'x' is zero, and the second solution is 8. Don't forget to check your answer by substituting the values for 'x' into the original equation to make sure you get a true statment because even super heros can make mistakes!

Now, back to the kidnapping. FOIL enters the code and saves the girls. Now his big moment has come. Time to get famous. But no one is exactly sure what he looks like maybe he should think about a new material for his costume.