{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-28T14:38:32+00:00","modifiedTime":"2016-03-28T14:38:32+00:00","timestamp":"2022-09-09T18:15:42+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Algebra","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33721"},"slug":"algebra","categoryId":33721}],"title":"How to Use UnFOIL to Factor Quadratic Equations","strippedTitle":"how to use unfoil to factor quadratic equations","slug":"how-to-use-unfoil-to-factor-quadratic-equations","canonicalUrl":"","seo":{"metaDescription":"Using the unFOIL method to factor quadratic equations into two binomials requires many steps. 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Remember that FOIL stands for first, outer, inner, and last.","blurb":"","authors":[],"primaryCategoryTaxonomy":{"categoryId":33721,"title":"Algebra","slug":"algebra","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33721"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[],"fromCategory":[{"articleId":255800,"title":"Applying the Distributive Property: Algebra Practice Questions","slug":"applying-the-distributive-property-algebra-practice-questions","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/255800"}},{"articleId":245778,"title":"Converting Improper and Mixed Fractions: Algebra Practice Questions","slug":"converting-improper-mixed-fractions-algebra-practice-questions","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/245778"}},{"articleId":210251,"title":"How to Calculate Limits with Algebra","slug":"how-to-calculate-limits-with-algebra","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/210251"}},{"articleId":210250,"title":"Understanding the Vocabulary of Algebra","slug":"understanding-the-vocabulary-of-algebra","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/210250"}},{"articleId":210249,"title":"Understanding Algebraic Variables","slug":"understanding-algebraic-variables","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/210249"}}]},"hasRelatedBookFromSearch":true,"relatedBook":{"bookId":282354,"slug":"linear-algebra-for-dummies","isbn":"9780470430903","categoryList":["academics-the-arts","math","algebra"],"amazon":{"default":"https://www.amazon.com/gp/product/0470430907/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/0470430907/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/0470430907-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/0470430907/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/0470430907/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/covers/9780470430903.jpg","width":250,"height":350},"title":"Linear Algebra For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"\n <p><p><b><b data-author-id=\"8985\">Mary Jane Sterling</b></b> taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. 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Prime factorization and order of decreasing powers are two parts of the unFOIL method, which helps you solve for quadratic equations. Remember that FOIL stands for first, outer, inner, and last.","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null},{"objectType":"article","id":167937,"data":{"title":"How to Solve a Quadratic Equation When It Won’t Factor","slug":"how-to-solve-a-quadratic-equation-when-it-wont-factor","update_time":"2016-03-26T15:12:02+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Pre-Calculus","slug":"pre-calculus","categoryId":33727}],"description":"When asked to solve a quadratic equation that you just can’t seem to factor (or that just doesn’t factor), you have to employ other ways of solving the equation, such as by using the quadratic formula. The quadratic formula is the formula used to solve for the variable in a quadratic equation in standard form. \nGiven a quadratic equation in standard form ax2 + bx + c = 0,\n\nBefore you apply the formula, it’s a good idea to rewrite the equation in standard form (if it isn’t already) and figure out the a, b, and c values.\nFor example, to solve x2 – 3x + 1 = 0, you first say that a = 1, b = –3, and c = 1. The a, b, and c terms simply plug into the formula to give you the values for x:\n\nSimplify this formula one time to get\n\nSimplify further to get your final answer, which is two x values (the x-intercepts):\n","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null},{"objectType":"article","id":138677,"data":{"title":"Factor a Quadratic Equation by Grouping Terms","slug":"factor-a-quadratic-equation-by-grouping-terms","update_time":"2016-03-26T07:10:03+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Algebra","slug":"algebra","categoryId":33721}],"description":"Factoring by grouping terms is a great method to use to rewrite a quadratic equation so that you can use the multiplication property of zero and find all the solutions. \nThe main idea behind factoring by grouping is to arrange the terms into smaller groupings that have a common factor. You go to little groupings because you can't find a greatest common factor for all the terms; however, by taking two terms at a time, you can find something to divide them by.\nFor example, look at the quadratic equation \n2x2 + 8x – 5x – 20 = 0, \nwhich has four terms. (Although you could combine the two middle terms on the left, in this case, leave them as is for the sake of the grouping process.)\nThe four terms in the equation don't share a greatest common factor. You can divide the first, second, and fourth terms evenly by 2, but the third term doesn't comply. The first three terms all have a factor of x, but the last term doesn't. So, you group the first two terms together and take out their common factor, 2x. The last two terms have a common factor of –5. The factored form, therefore, is \n2x(x + 4) – 5(x + 4) = 0.\nThe new, factored form has two terms. Each of the terms has an (x + 4) factor, so you can divide that factor out of each term. When you divide the first term, you have 2x left. When you divide the second term, you have –5 left. Your new factored form is \n(x + 4)(2x – 5) = 0. \nNow you can set each factor equal to zero to get \n\nKeep in mind that factoring by grouping works only when you can create a new form of the quadratic equation that has fewer terms and a common factor. If the factor (x + 4) hadn't shown up in both of the factored terms in this example, you would've gone in a different direction.\nSolving quadratic equations by grouping and factoring is even more important when the exponents in the equations get larger. For example, the equation \n5x3 + x2 – 45x – 9 = 0\nis a third-degree equation (the highest power on any of the variables is 3), so it has the potential for three different solutions. You can't find a factor common to all four terms, so you group the first two terms, factor out x2, group the last two terms, and factor out –9. The factored equation is\nx2(5x + 1) – 9(5x + 1) = 0\nThe common factor of the two terms in the new equation is (5x + 1), so you divide it out of the two terms to get \n(5x + 1)(x2 – 9) = 0\nThe second factor is the difference of squares, so you can rewrite the equation as \n(5x + 1)(x – 3)(x + 3) = 0\nThe three solutions are \n","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null},{"objectType":"article","id":192154,"data":{"title":"How to Solve (and Factor) a Quadratic Equation with the Quadratic Formula","slug":"how-to-solve-and-factor-a-quadratic-equation-with-the-quadratic-formula","update_time":"2016-03-26T21:19:00+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Calculus","slug":"calculus","categoryId":33723}],"description":"A quadratic equation is any second-degree polynomial equation — that’s when the highest power of x, or whatever other variable is used, is 2. The solution or solutions of a quadratic equation,\n\n\nSolve the equation,\n\nwith the quadratic formula:\n\n Bring all terms to one side of the equation, leaving a zero on the other side.\n\n \n Plug the coefficients into the formula.\nIn this example, a equals 2, b is –5, and c is –12, so\n\n \n\nYou can also use the quadratic formula for factoring trinomials. \n\nHere’s what you do.\n\n Use the quadratic formula to get solutions for x. (You can also use your calculator to get the solutions.) Make sure the solutions are written as fractions rather than as decimals and that they’re reduced to lowest terms.\n\n \n Take the two solutions and put them in factors. If a solution is positive, use subtraction. If a solution is negative, use addition.\n\n \n If either solution is a fraction, take the denominator and bring it in front of the x.\n\nAnd, voilà, the trinomial is factored:\n(x – 4)(2x + 3) \n \n","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null},{"objectType":"article","id":194263,"data":{"title":"How to Factor a Trinomial by UnFOILing","slug":"how-to-factor-a-trinomial-by-unfoiling","update_time":"2016-03-26T21:47:11+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Algebra","slug":"algebra","categoryId":33721}],"description":"UnFOILing is a method for factoring a trinomial into two binomials. When you multiply two binomials together, you use the FOIL method, multiplying the First, then the Outer, then the Inner, and finally the Last terms of the two binomials into a trinomial. But when you need to factor a trinomial, you unFOIL by determining the factor pairs for a and c, the correct signs to place inside the two binomials, and what combination of factor pairs of a and c results in b.\nThe key to unFOILing is being organized:\n\n Be sure you have an expression in the form: \n\n \n Write the terms in the order of decreasing powers.\n\n \n Remember how to assign the correct signs in each binomial:\n \n The signs are both positive, if c is positive and b is positive.\n \n The signs are both negative, if c is positive and b is negative.\n \n One sign is positive and one negative, if c is negative; which binomial is positive and which one is negative depends on whether b is positive or negative and how you arranged the factors.\n \n \n \n\nExample: \n\n\n Determine all the ways you can multiply two numbers to get a.\nYou can get these numbers from the prime factorization of a. Sometimes, writing out the list of ways to multiply is a big help. In this example, a is 24, and the list of ways you can multiply two numbers to get 24 is:\n1 × 24, 2 × 12, 3 × 8, or 4 × 6.\n \n Determine all the ways you can multiply two numbers to get c.\nIn this example, c is 45, and you can multiply the following numbers to get 45:\n1 × 45, 3 × 15, or 5 × 9.\nIgnore the sign at this point. You don't need to worry about signs until Step 3.\n \n Look at the sign of c and your lists from Steps 1 and 2 to see if you want a sum or difference.\nIf c is positive, find a value from your Step 1 list and another from your Step 2 list such that the sum of their product and the product of the two remaining numbers in those steps results in b.\nIf c is negative, find a value from your Step 1 list and another from your Step 2 list such that the difference of their product and the product of two remaining numbers from those steps results in b.\nFor the trinomial \n\nc is negative, so you want a difference of 34 between products.\n \n Choose a product from Step 1 and a product from Step 2 that result in the correct sum or difference determined in Step 3.\nBecause you determined in Step 3 that you want a difference of 34 between products, use 4 × 6 from a and 5 × 9 from c.\nThe product of 4 and 5 is 20. The product of 6 and 9 is 54. The difference of these products is 34.\n \n Arrange your choices as binomials so the results are those you want.\n(4x 9)(6x 5)\n \n Place the signs to give the desired results.\n(4x – 9)(6x + 5)\n \n FOIL the two binomials to check your work.\nIf the binomials are correct, you'll end up with the original problem when you FOIL them.\n\n \n","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null}]},"relatedArticlesStatus":"success"},"routeState":{"name":"Article3","path":"/article/academics-the-arts/math/algebra/how-to-use-unfoil-to-factor-quadratic-equations-210247/","hash":"","query":{},"params":{"category1":"academics-the-arts","category2":"math","category3":"algebra","article":"how-to-use-unfoil-to-factor-quadratic-equations-210247"},"fullPath":"/article/academics-the-arts/math/algebra/how-to-use-unfoil-to-factor-quadratic-equations-210247/","meta":{"routeType":"article","breadcrumbInfo":{"suffix":"Articles","baseRoute":"/category/articles"},"prerenderWithAsyncData":true},"from":{"name":null,"path":"/","hash":"","query":{},"params":{},"fullPath":"/","meta":{}}},"dropsState":{"submitEmailResponse":false,"status":"initial"},"profileState":{"auth":{},"userOptions":{},"status":"success"}}# How to Use UnFOIL to Factor Quadratic Equations

Using the unFOIL method to factor quadratic equations into two binomials requires many steps. Prime factorization and order of decreasing powers are two parts of the unFOIL method, which helps you solve for quadratic equations. Remember that FOIL stands for first, outer, inner, and last. ## About This Article

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