{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2017-01-28T00:56:07+00:00","modifiedTime":"2017-01-28T00:56:07+00:00","timestamp":"2022-09-14T18:17:09+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":"Study Skills & Test Prep","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33772"},"slug":"study-skills-test-prep","categoryId":33772},{"name":"SAT","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33794"},"slug":"sat","categoryId":33794}],"title":"SAT Practice Questions: Solving Quadratic Functions","strippedTitle":"sat practice questions: solving quadratic functions","slug":"sat-practice-questions-solving-quadratic-functions","canonicalUrl":"","seo":{"metaDescription":"On the SAT Math exam, you will probably encounter a quadratic function or two, so it’s important to remember that they come in two forms: y = ax 2 + bx + c or f","noIndex":0,"noFollow":0},"content":"On the SAT Math exam, you will probably encounter a quadratic function or two, so it’s important to remember that they come in two forms: <em>y</em> = <em>ax<sup>2</sup></em> + <em>bx</em> + <em>c</em> or <em>f</em> (<em>x</em>) = <em>ax<sup>2</sup></em> + <em>bx</em> + <em>c</em>. (Don’t panic; they mean the same thing.)\r\n\r\nThe following practice questions may look scary, but they simply involve a little distribution, simplifying, and plugging in of values.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li><strong>Given this equation, what is the value of <em>a</em> + <em>b</em> + <em>c</em>?</strong>\r\n<em>x</em>(2<em>x</em> + 3) – 2(<em>x</em> – 3) = <em>ax</em><sup>2</sup> + <em>bx</em> + <em>c</em></li>\r\n\t<li><strong>If <em>a</em>, <em>b</em>, and <em>c</em> are integers, 6<em>x</em><sup>2</sup> + <em>cx</em> + 6 = (<em>ax</em> + 2)(<em>bx</em> + 3) for all values of <em>x</em>, and 1 < <em>a</em> < <em>b</em>, what is the value of <em>c</em>?</strong></li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n\t<li><strong>The correct answer is 9.</strong>\r\nDistribute and simplify the expressions on the left to match the quadratic on the right:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_0601.gif\"><img class=\"alignnone size-full wp-image-232665\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_0601.gif\" alt=\"SAT1001_eq0601\" width=\"235\" height=\"80\" /></a>\r\nFrom this, you know that <em>a</em> = 2, <em>b</em> = 1, and <em>c</em> = 6, which add up to 9.</li>\r\n\t<li><strong>The correct answer is 12.</strong>\r\nMultiply the binomials to match the quadratic, and then simplify by subtracting 6 from both sides:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_0602.gif\"><img class=\"alignnone size-full wp-image-232666\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_0602.gif\" alt=\"SAT1001_eq0602\" width=\"243\" height=\"116\" /></a>\r\nBecause 6<em>x</em><sup>2</sup> = <em>abx</em><sup>2</sup>, <em>ab</em> = 6. And because <em>a</em> and <em>b</em> are integers and 1 < <em>a</em> < <em>b</em>, you know that <em>a</em> = 2 and <em>b</em> = 3. Now, using <em>cx</em> = (3<em>a</em> + 2<em>b</em>)<em>x</em>, you can plug in 2 for <em>a</em> and 3 for <em>b</em> and then solve for <em>c</em>:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_0603.gif\"><img class=\"alignnone size-full wp-image-232667\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_0603.gif\" alt=\"SAT1001_eq0603\" width=\"135\" height=\"113\" /></a></li>\r\n</ol>","description":"On the SAT Math exam, you will probably encounter a quadratic function or two, so it’s important to remember that they come in two forms: <em>y</em> = <em>ax<sup>2</sup></em> + <em>bx</em> + <em>c</em> or <em>f</em> (<em>x</em>) = <em>ax<sup>2</sup></em> + <em>bx</em> + <em>c</em>. (Don’t panic; they mean the same thing.)\r\n\r\nThe following practice questions may look scary, but they simply involve a little distribution, simplifying, and plugging in of values.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li><strong>Given this equation, what is the value of <em>a</em> + <em>b</em> + <em>c</em>?</strong>\r\n<em>x</em>(2<em>x</em> + 3) – 2(<em>x</em> – 3) = <em>ax</em><sup>2</sup> + <em>bx</em> + <em>c</em></li>\r\n\t<li><strong>If <em>a</em>, <em>b</em>, and <em>c</em> are integers, 6<em>x</em><sup>2</sup> + <em>cx</em> + 6 = (<em>ax</em> + 2)(<em>bx</em> + 3) for all values of <em>x</em>, and 1 < <em>a</em> < <em>b</em>, what is the value of <em>c</em>?</strong></li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n\t<li><strong>The correct answer is 9.</strong>\r\nDistribute and simplify the expressions on the left to match the quadratic on the right:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_0601.gif\"><img class=\"alignnone size-full wp-image-232665\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_0601.gif\" alt=\"SAT1001_eq0601\" width=\"235\" height=\"80\" /></a>\r\nFrom this, you know that <em>a</em> = 2, <em>b</em> = 1, and <em>c</em> = 6, which add up to 9.</li>\r\n\t<li><strong>The correct answer is 12.</strong>\r\nMultiply the binomials to match the quadratic, and then simplify by subtracting 6 from both sides:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_0602.gif\"><img class=\"alignnone size-full wp-image-232666\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_0602.gif\" alt=\"SAT1001_eq0602\" width=\"243\" height=\"116\" /></a>\r\nBecause 6<em>x</em><sup>2</sup> = <em>abx</em><sup>2</sup>, <em>ab</em> = 6. And because <em>a</em> and <em>b</em> are integers and 1 < <em>a</em> < <em>b</em>, you know that <em>a</em> = 2 and <em>b</em> = 3. Now, using <em>cx</em> = (3<em>a</em> + 2<em>b</em>)<em>x</em>, you can plug in 2 for <em>a</em> and 3 for <em>b</em> and then solve for <em>c</em>:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_0603.gif\"><img class=\"alignnone size-full wp-image-232667\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_0603.gif\" alt=\"SAT1001_eq0603\" width=\"135\" height=\"113\" /></a></li>\r\n</ol>","blurb":"","authors":[{"authorId":8978,"name":"Ron Woldoff","slug":"ron-woldoff","description":" <p><b>Ron Woldoff is founder of National Test Prep, where he helps students succeed on the GMAT, GRE, SAT, ACT, and PSAT. He’s the author of numerous Dummies test prep titles, including <i>GRE 2022 For Dummies</i> and <i>SAT: 1,001 Practice Questions For Dummies.</i></p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8978"}}],"primaryCategoryTaxonomy":{"categoryId":33794,"title":"SAT","slug":"sat","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33794"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":232868,"title":"SAT Writing Practice Problems: Parallel Structure, Agreement, and Tense","slug":"sat-writing-practice-problems-parallel-structure-agreement-tense","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/232868"}},{"articleId":232865,"title":"SAT Writing Practice Problems: Logic and Organization","slug":"sat-writing-practice-problems-logic-organization","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/232865"}},{"articleId":232862,"title":"SAT Writing Practice Problems: Vocabulary in Context","slug":"sat-writing-practice-problems-vocabulary-context","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/232862"}},{"articleId":232859,"title":"SAT Writing Practice Problems: Grammar and Punctuation","slug":"sat-writing-practice-problems-grammar-punctuation","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/232859"}},{"articleId":232855,"title":"SAT Reading Practice Problems: Interpreting Visual Elements","slug":"sat-reading-practice-problems-interpreting-visual-elements","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/232855"}}],"fromCategory":[{"articleId":293029,"title":"SAT Prep 2023 For Dummies Cheat Sheet","slug":"sat-prep-2023-for-dummies-cheat-sheet","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/293029"}},{"articleId":277844,"title":"10 Ways to Get the Most from the Practice SATs","slug":"10-ways-to-get-the-most-from-the-practice-sats","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/277844"}},{"articleId":277839,"title":"10 Mistakes You Won’t Make on the SAT","slug":"10-mistakes-you-wont-make-on-the-sat","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/277839"}},{"articleId":277836,"title":"Strategies for the SAT Reading Test","slug":"strategies-for-the-sat-reading-test","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/277836"}},{"articleId":277833,"title":"Simple Strategies for Taking the SAT Writing and Language Test","slug":"simple-strategies-for-taking-the-sat-writing-and-language-test","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/277833"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282560,"slug":"sat-1001-practice-questions-for-dummies","isbn":"9781119215844","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"amazon":{"default":"https://www.amazon.com/gp/product/1119215846/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119215846/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/1119215846-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119215846/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119215846/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/sat-1001-practice-questions-for-dummies-cover-9781119215844-202x255.jpg","width":202,"height":255},"title":"SAT","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p>Ron Woldoff is the founder of National Test Prep, where he helps students prepare for the SAT, GMAT, and GRE. He is the author of several books, including <i>GRE For Dummies</i> and <i>1,001 GRE Practice Questions For Dummies</i>.</p>","authors":[{"authorId":8978,"name":"Ron Woldoff","slug":"ron-woldoff","description":" <p><b>Ron Woldoff is founder of National Test Prep, where he helps students succeed on the GMAT, GRE, SAT, ACT, and PSAT. He’s the author of numerous Dummies test prep titles, including <i>GRE 2022 For Dummies</i> and <i>SAT: 1,001 Practice Questions For Dummies.</i></p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8978"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","study-skills-test-prep","sat"]},{"key":"isbn","values":["9781119215844"]}]\" id=\"du-slot-63221aa517f51\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","study-skills-test-prep","sat"]},{"key":"isbn","values":["9781119215844"]}]\" id=\"du-slot-63221aa51853f\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":null,"lifeExpectancySetFrom":null,"dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":232664},"articleLoadedStatus":"success"},"listState":{"list":{},"objectTitle":"","status":"initial","pageType":null,"objectId":null,"page":1,"sortField":"time","sortOrder":1,"categoriesIds":[],"articleTypes":[],"filterData":{},"filterDataLoadedStatus":"initial","pageSize":10},"adsState":{"pageScripts":{"headers":{"timestamp":"2024-03-04T05:50:01+00:00"},"adsId":0,"data":{"scripts":[{"pages":["all"],"location":"header","script":"\r\n<script src=\"https://cdn.optimizely.com/js/10563184655.js\"></script>","enabled":false},{"pages":["all"],"location":"header","script":"\r\n<script>var _comscore = _comscore || [];_comscore.push({ c1: \"2\", c2: \"15097263\" });(function() {var s = document.createElement(\"script\"), el = document.getElementsByTagName(\"script\")[0]; s.async = true;s.src = (document.location.protocol == \"https:\" ? \"https://sb\" : \"http://b\") + \".scorecardresearch.com/beacon.js\";el.parentNode.insertBefore(s, el);})();</script><noscript><img src=\"https://sb.scorecardresearch.com/p?c1=2&c2=15097263&cv=2.0&cj=1\" /></noscript>\r\n","enabled":true},{"pages":["all"],"location":"footer","script":"\r\n<script type='text/javascript'>\r\n(function(){var g=function(e,h,f,g){\r\nthis.get=function(a){for(var a=a+\"=\",c=document.cookie.split(\";\"),b=0,e=c.length;b<e;b++){for(var d=c[b];\" \"==d.charAt(0);)d=d.substring(1,d.length);if(0==d.indexOf(a))return d.substring(a.length,d.length)}return null};\r\nthis.set=function(a,c){var b=\"\",b=new Date;b.setTime(b.getTime()+6048E5);b=\"; expires=\"+b.toGMTString();document.cookie=a+\"=\"+c+b+\"; path=/; \"};\r\nthis.check=function(){var a=this.get(f);if(a)a=a.split(\":\");else if(100!=e)\"v\"==h&&(e=Math.random()>=e/100?0:100),a=[h,e,0],this.set(f,a.join(\":\"));else return!0;var c=a[1];if(100==c)return!0;switch(a[0]){case \"v\":return!1;case \"r\":return c=a[2]%Math.floor(100/c),a[2]++,this.set(f,a.join(\":\")),!c}return!0};\r\nthis.go=function(){if(this.check()){var a=document.createElement(\"script\");a.type=\"text/javascript\";a.src=g;document.body&&document.body.appendChild(a)}};\r\nthis.start=function(){var t=this;\"complete\"!==document.readyState?window.addEventListener?window.addEventListener(\"load\",function(){t.go()},!1):window.attachEvent&&window.attachEvent(\"onload\",function(){t.go()}):t.go()};};\r\ntry{(new g(100,\"r\",\"QSI_S_ZN_5o5yqpvMVjgDOuN\",\"https://zn5o5yqpvmvjgdoun-wiley.siteintercept.qualtrics.com/SIE/?Q_ZID=ZN_5o5yqpvMVjgDOuN\")).start()}catch(i){}})();\r\n</script><div id='ZN_5o5yqpvMVjgDOuN'></div>\r\n","enabled":false},{"pages":["all"],"location":"header","script":"\r\n<script>\r\n (function(h,o,t,j,a,r){\r\n h.hj=h.hj||function(){(h.hj.q=h.hj.q||[]).push(arguments)};\r\n h._hjSettings={hjid:257151,hjsv:6};\r\n a=o.getElementsByTagName('head')[0];\r\n r=o.createElement('script');r.async=1;\r\n r.src=t+h._hjSettings.hjid+j+h._hjSettings.hjsv;\r\n a.appendChild(r);\r\n })(window,document,'https://static.hotjar.com/c/hotjar-','.js?sv=');\r\n</script>","enabled":false},{"pages":["article"],"location":"header","script":" <script src=\"//get.s-onetag.com/bffe21a1-6bb8-4928-9449-7beadb468dae/tag.min.js\" async defer></script>","enabled":true},{"pages":["homepage"],"location":"header","script":"<meta name=\"facebook-domain-verification\" content=\"irk8y0irxf718trg3uwwuexg6xpva0\" />","enabled":true},{"pages":["homepage","article","category","search"],"location":"footer","script":"\r\n<noscript>\r\n<img height=\"1\" width=\"1\" src=\"https://www.facebook.com/tr?id=256338321977984&ev=PageView&noscript=1\"/>\r\n</noscript>\r\n","enabled":true}]}},"pageScriptsLoadedStatus":"success"},"navigationState":{"navigationCollections":[{"collectionId":287568,"title":"BYOB (Be Your Own Boss)","hasSubCategories":false,"url":"/collection/for-the-entry-level-entrepreneur-287568"},{"collectionId":293237,"title":"Be a Rad Dad","hasSubCategories":false,"url":"/collection/be-the-best-dad-293237"},{"collectionId":295890,"title":"Career Shifting","hasSubCategories":false,"url":"/collection/career-shifting-295890"},{"collectionId":294090,"title":"Contemplating the Cosmos","hasSubCategories":false,"url":"/collection/theres-something-about-space-294090"},{"collectionId":287563,"title":"For Those Seeking Peace of Mind","hasSubCategories":false,"url":"/collection/for-those-seeking-peace-of-mind-287563"},{"collectionId":287570,"title":"For the Aspiring Aficionado","hasSubCategories":false,"url":"/collection/for-the-bougielicious-287570"},{"collectionId":291903,"title":"For the Budding Cannabis Enthusiast","hasSubCategories":false,"url":"/collection/for-the-budding-cannabis-enthusiast-291903"},{"collectionId":299891,"title":"For the College Bound","hasSubCategories":false,"url":"/collection/for-the-college-bound-299891"},{"collectionId":291934,"title":"For the Exam-Season Crammer","hasSubCategories":false,"url":"/collection/for-the-exam-season-crammer-291934"},{"collectionId":301547,"title":"For the Game Day Prepper","hasSubCategories":false,"url":"/collection/big-game-day-prep-made-easy-301547"}],"navigationCollectionsLoadedStatus":"success","navigationCategories":{"books":{"0":{"data":[{"categoryId":33512,"title":"Technology","hasSubCategories":true,"url":"/category/books/technology-33512"},{"categoryId":33662,"title":"Academics & The Arts","hasSubCategories":true,"url":"/category/books/academics-the-arts-33662"},{"categoryId":33809,"title":"Home, Auto, & Hobbies","hasSubCategories":true,"url":"/category/books/home-auto-hobbies-33809"},{"categoryId":34038,"title":"Body, Mind, & Spirit","hasSubCategories":true,"url":"/category/books/body-mind-spirit-34038"},{"categoryId":34224,"title":"Business, Careers, & Money","hasSubCategories":true,"url":"/category/books/business-careers-money-34224"}],"breadcrumbs":[],"categoryTitle":"Level 0 Category","mainCategoryUrl":"/category/books/level-0-category-0"}},"articles":{"0":{"data":[{"categoryId":33512,"title":"Technology","hasSubCategories":true,"url":"/category/articles/technology-33512"},{"categoryId":33662,"title":"Academics & The Arts","hasSubCategories":true,"url":"/category/articles/academics-the-arts-33662"},{"categoryId":33809,"title":"Home, Auto, & Hobbies","hasSubCategories":true,"url":"/category/articles/home-auto-hobbies-33809"},{"categoryId":34038,"title":"Body, Mind, & Spirit","hasSubCategories":true,"url":"/category/articles/body-mind-spirit-34038"},{"categoryId":34224,"title":"Business, Careers, & Money","hasSubCategories":true,"url":"/category/articles/business-careers-money-34224"}],"breadcrumbs":[],"categoryTitle":"Level 0 Category","mainCategoryUrl":"/category/articles/level-0-category-0"}}},"navigationCategoriesLoadedStatus":"success"},"searchState":{"searchList":[],"searchStatus":"initial","relatedArticlesList":[],"relatedArticlesStatus":"initial"},"routeState":{"name":"Article3","path":"/article/academics-the-arts/study-skills-test-prep/sat/sat-practice-questions-solving-quadratic-functions-232664/","hash":"","query":{},"params":{"category1":"academics-the-arts","category2":"study-skills-test-prep","category3":"sat","article":"sat-practice-questions-solving-quadratic-functions-232664"},"fullPath":"/article/academics-the-arts/study-skills-test-prep/sat/sat-practice-questions-solving-quadratic-functions-232664/","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"}}

SAT Practice Questions: Solving Quadratic Functions

By: Ron Woldoff and

Updated: 01-28-2017

From The Book: SAT

SAT

Book image

Explore Book Buy On Amazon

On the SAT Math exam, you will probably encounter a quadratic function or two, so it’s important to remember that they come in two forms: y = ax² + bx + c or f (x) = ax² + bx + c. (Don’t panic; they mean the same thing.)

The following practice questions may look scary, but they simply involve a little distribution, simplifying, and plugging in of values.

Practice questions

Given this equation, what is the value of a + b + c? x(2x + 3) – 2(x – 3) = ax² + bx + c
If a, b, and c are integers, 6x² + cx + 6 = (ax + 2)(bx + 3) for all values of x, and 1 < a < b, what is the value of c?

Answers and explanations

The correct answer is 9. Distribute and simplify the expressions on the left to match the quadratic on the right:
From this, you know that a = 2, b = 1, and c = 6, which add up to 9.
The correct answer is 12. Multiply the binomials to match the quadratic, and then simplify by subtracting 6 from both sides:
Because 6x² = abx², ab = 6. And because a and b are integers and 1 < a < b, you know that a = 2 and b = 3. Now, using cx = (3a + 2b)x, you can plug in 2 for a and 3 for b and then solve for c:

About This Article

This article is from the book:

SAT ,

About the book author:

Ron Woldoff is the founder of National Test Prep, where he helps students prepare for the SAT, GMAT, and GRE. He is the author of several books, including GRE For Dummies and 1,001 GRE Practice Questions For Dummies.

This article can be found in the category:

SAT ,