But no one is exactly sure what he looks like maybe he should think about a new material for his costume. FOIL enters the code and saves the girls. 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! The first solution for 'x' is zero, and the second solution is 8. To solve, you can factor out the greatest common factor, which is 'x'. This problem looks different because it has no constant. I know you're anxious to find out what’s happening on the dock, but be patient. For this equation there is just one solution, x equals 2. Now use the reverse of FOIL to factor, and then apply the Zero Factor Property to find the solutions for the variable. For this first problem, modify the equation to write it in standard form to set the equation equal to zero. Let’s try some more problems and investigate some strategies to make these calculations easier to work with. By using opposite operations, he gets two answers for 'x', -3 and 2. He sets each binomial factor to zero and solves for 'x' in each case. To calculate the solution and free the girls, he must use the Zero Factor Property. Although he's figured out the factors, he doesn't have a solution. As always, it’s a good idea to check your work by FOILing. So we factored our quadratic equation into two binomials (x-2) and (x+3). 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. 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. So now we have to find factors of -6 that sum to 1. Therefore, 'm' plus 'n' have to be equal to 1. In our example, m(n) = -6 and mx + nx = 1x. We have to find the values for the variables 'm' and 'n'. To factor this quadratic equation we can use the 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. When you plug either of these two values into the original equation, you should get 0. If you use opposite operations, you should get two answers for x, -6 and 1. Set each set of parentheses equal to zero. It's important that you always set the expression equal to zero, otherwise this rule won’t work. In this example, either one or both of the factors have to be zero to get a true statement. Let’s start by having a look at the Zero Factor Property. To figure it out, FOIL must find the solutions for this quadratic equation. The girls are locked up in a container secured by a very complicated code. 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?įOIL will need his calculator, his super smarts and how to solve quadratic equations by factoring. What’s that, you ask? Hold on to that thought. 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. People pass by him, but no one seems to notice the inconspicuous man. When you watch this video, you will see a clearer picture of solving quadratic equations by factoring with concrete examples.Īnalyze Functions Using Different Representations.Įvery day in San Francisco, on Pier 39, there is a street performer named FOIL. Replace x with either values of the roots in the original equation to check. Using the reverse FOIL method, find the factors of c (m and n) that will make both of the following statements true: m * n = c and m + n = b.Įxpress the equation in the form (x + m)(x + n) = 0.īecause of the zero property, we can equate x + m = 0 and x + n = 0. So, if we are given the quadratic equation: x 2 + bx + c = 0, we just need to do the following: The FOIL method tells us that (x + m)(x + n) = x 2 + nx + mx + mn = x 2 + (n + m)x + nm. The zero property of multiplication tells us that if at least one of the factors is equal to zero, then the product is equal to zero. These two techniques come in handy when using the factoring method for solving quadratic equations. You may also recall that the FOIL method is a handy tool when multiplying two binomials. By this time, you may already be familiar with the zero property of multiplication.
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