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. Please purchase additional licenses if you intend to share this product.By this time, you may already be familiar with the zero property of multiplication.
Permission to copy for single classroom use only. Solving Quadratic Equations Choice Board Digital & Printable Solving Quadratic Equations by Factoring Guided Notes Solving Quadratic Equations by Factoring Pixel Art ➡️ Colored in image to see how the image is supposed to lookĬheck out the thumbnails and preview to see the types of problems. ➡️ 20×20 grid with a pattern for students to color
Each question has 3 answer choices for students to select from. The question boxes have plenty of space for students to show their work. This is an engaging no prep, self-checking activity for your students to practice what you have taught them about multiplying polynomials! This color by number pixel art activity is perfect for a day when you need a sub! As they continue to answer and color the grid, the image will be more clear. As students work through each question, their answers will tell them how to color the grid. This color by number pixel art activity is perfect for students who are learning how to solve quadratic equations by factoring. Please contact the seller about any problems with your order using the question button below the description. Files will be available for download from your account once payment is confirmed.