{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2017-01-28T03:24:35+00:00","modifiedTime":"2017-01-28T03:24:35+00:00","timestamp":"2022-09-14T18:17:10+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: Factoring","strippedTitle":"sat practice questions: factoring","slug":"sat-practice-questions-factoring","canonicalUrl":"","seo":{"metaDescription":"The SAT Math exam contains questions where you'll need to know how to factor down a quadratic equation. The following practice questions ask you to do that, and","noIndex":0,"noFollow":0},"content":"The SAT Math exam contains questions where you'll need to know how to factor down a quadratic equation. The following practice questions ask you to do that, and then to plug in your solution to solve a given expression.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li>What is the value of\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_2001.gif\"><img class=\"alignnone size-full wp-image-232783\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_2001.gif\" alt=\"SAT1001_eq2001\" width=\"43\" height=\"23\" /></a>\r\nif a – b = 1/3 and a + b = 6?</li>\r\n\t<li>What is the value of p2 + q2 if p2 – q2 = 7 and p4 – q4 = 28?\r\nA. 2\r\nB. 3\r\nC. 4\r\nD. 5</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n\t<li>The correct answer is 25.\r\nRemember that a2 – b2 = (a + b)(a – b). Plug in the values of a + b and a – b to solve for a2 – b2:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_2002.gif\"><img class=\"alignnone size-full wp-image-232784\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_2002.gif\" alt=\"SAT1001_eq2002\" width=\"123\" height=\"75\" /></a>\r\nNow plug 2 in for a2 – b2:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_2003.gif\"><img class=\"alignnone size-full wp-image-232785\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_2003.gif\" alt=\"SAT1001_eq2003\" width=\"116\" height=\"23\" /></a></li>\r\n\t<li>The correct answer is Choice (C).\r\nStart by factoring p4 – q4:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_2004.gif\"><img class=\"alignnone size-full wp-image-232786\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_2004.gif\" alt=\"SAT1001_eq2004\" width=\"205\" height=\"31\" /></a>\r\nNow plug in the values that the question gives you:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_2005.gif\"><img class=\"alignnone size-full wp-image-232787\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_2005.gif\" alt=\"SAT1001_eq2005\" width=\"209\" height=\"92\" /></a></li>\r\n</ol>","description":"The SAT Math exam contains questions where you'll need to know how to factor down a quadratic equation. The following practice questions ask you to do that, and then to plug in your solution to solve a given expression.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li>What is the value of\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_2001.gif\"><img class=\"alignnone size-full wp-image-232783\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_2001.gif\" alt=\"SAT1001_eq2001\" width=\"43\" height=\"23\" /></a>\r\nif a – b = 1/3 and a + b = 6?</li>\r\n\t<li>What is the value of p2 + q2 if p2 – q2 = 7 and p4 – q4 = 28?\r\nA. 2\r\nB. 3\r\nC. 4\r\nD. 5</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n\t<li>The correct answer is 25.\r\nRemember that a2 – b2 = (a + b)(a – b). Plug in the values of a + b and a – b to solve for a2 – b2:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_2002.gif\"><img class=\"alignnone size-full wp-image-232784\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_2002.gif\" alt=\"SAT1001_eq2002\" width=\"123\" height=\"75\" /></a>\r\nNow plug 2 in for a2 – b2:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_2003.gif\"><img class=\"alignnone size-full wp-image-232785\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_2003.gif\" alt=\"SAT1001_eq2003\" width=\"116\" height=\"23\" /></a></li>\r\n\t<li>The correct answer is Choice (C).\r\nStart by factoring p4 – q4:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_2004.gif\"><img class=\"alignnone size-full wp-image-232786\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_2004.gif\" alt=\"SAT1001_eq2004\" width=\"205\" height=\"31\" /></a>\r\nNow plug in the values that the question gives you:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_2005.gif\"><img class=\"alignnone size-full wp-image-232787\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_2005.gif\" alt=\"SAT1001_eq2005\" width=\"209\" height=\"92\" /></a></li>\r\n</ol>","blurb":"","authors":[{"authorId":8978,"name":"Ron Woldoff","slug":"ron-woldoff","description":" Ron Woldoff is founder of National Test Prep, where he helps students succeed on the GMAT, GRE, SAT, ACT, and PSAT. 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SAT Practice Questions: Factoring

By: Ron Woldoff and

Updated: 01-28-2017

From The Book: SAT

SAT

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The SAT Math exam contains questions where you'll need to know how to factor down a quadratic equation. The following practice questions ask you to do that, and then to plug in your solution to solve a given expression.

Practice questions

What is the value of
if a – b = 1/3 and a + b = 6?
What is the value of p² + q² if p² – q² = 7 and p⁴ – q⁴ = 28? A. 2 B. 3 C. 4 D. 5

Answers and explanations

The correct answer is 25. Remember that a²– b² = (a + b)(a – b). Plug in the values of a + b and a – b to solve for a² – b²:
Now plug 2 in for a² – b²:
The correct answer is Choice (C). Start by factoring p⁴ – q⁴:
Now plug in the values that the question gives you:

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.

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