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UW Stout MATH 110 - Homework Problems

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Please pass your Sec. 6.6 homework worksheets to the center aisle to be picked up.Math TLC Open Lab Hours:Review for Test 3NOTICE:Test 3 covers Chapter 6 (Rational Expressions) This test is worth 70 points, and the practice test is worth another 7 points as usual. (Your best score on the practice test will earn that percentage of 7points.)Warning!To study for the test:Another good study aid: “Chapter Highlights” pages in book: Ch. 6: pages 403-406 (skip 6.7 ) (You can find these in either the on-line or the paper textbook.)IMPORTANT:REVIEW: Strategy for Factoring a Polynomial:Slide 11Domain example:Slide 13Slide 14Slide 15Slide 16Slide 17Example: Solving a rational equation:Example (continued):Reminders:Slide 21Slide 22Slide 23Please pass your Sec. 6.6 homework worksheets to the center aisle to be picked up.Any questions on the 6.6 homework problems?Math TLC Open Lab Hours:Room 203 Jarvis Hall Science WingMonday through Thursday 8:00 a.m. – 6:30 p.m._______________________________________________________________________________________________________________Review for Test 3NOTICE:No Ipods or other devices with earphones are to be used during tests or quizzes. Please turn off and put away these devices, including cell phones, before you log in to take the test on Monday.Test 3 covers Chapter 6 (Rational Expressions)This test is worth 70 points, and the practice test is worth another 7 points as usual. (Your best score on the practice test will earn that percentage of 7points.)Warning!Don’t forget to review the application problems from section 6.6 homework and your work on the offline worksheet. (Remember those fun problems about planes and cars, and three people doing a job at different rates?) These were a common source of trouble for many students in previous semesters, so make sure you study the application problems on the Practice Test, and then review the section 6.6 homework if you need more work on those problems.To study for the test:1). Take Practice Test 3 as many times as you want. Take notes as you go, and remember that you can REVIEW each version as many times as you want using “Check My Grades”. There are 20 questions on the practice test (vs. 15 on the real test.) Each time you take the practice test you will get a different set of questions, so taking it at least twice will help you review most topics that will be covered on the test.2). Review the homework from the sections in which you missed questions on the practice test. (After you take the practice quiz one or more times, use the “My Study Plan” button to get access to a customized set of problems for the topics you missed on the practice test.) 3). Review your notes and/or the online lecture slides (under each Assignment).Another good study aid:“Chapter Highlights” pages in book:Ch. 6: pages 403-406 (skip 6.7 ) (You can find these in either the on-line or the paper textbook.)IMPORTANT:Almost all problems in Chapter 6 on rational expressions require you to use one or more techniques for factoring polynomials. DON’T FORGET TO REVIEW THESE FACTORING METHODS AND KNOW HOW AND WHEN TO USE EACH ONE!Two methods that students often need to review are factoring by grouping and sums/differences of cubes, so make sure you know these methods and when to use them.REVIEW: Strategy for Factoring a Polynomial:1. Always look first to see if there is a common factor. If so, factor out the GCF.2. Determine the number of terms in the polynomial and try factoring as follows:a) If there are two terms, can the binomial be factored by one of the special formulas including difference of two squares, sum of two cubes, or difference of two cubes? (Use formula sheet!)b) If there are three terms, is the trinomial a perfect square trinomial? If the trinomial is not a perfect square trinomial, try factoring by the British (factoring by grouping) method.c) If there are four or more terms, try factoring by grouping.3. Check to see if any factors with more than one term in the factored polynomial can be factored further. If so, factor completely.REMINDER: You will be given the sheet containing formulas to use on quizzes/tests. You can print off a copy of the formula sheet to use while you do your homework and practice quizzes/tests by clicking on the “Formula sheet” menu button (or ask for a copy of the yellow handout version available in class.) This is especially useful on this test for the sum of cubes and difference of cubes formulas.Domain example:Find the domain of the expression204322xxxxSolution: Set the denominator equal to zero and solve for x. (Notice that this boils down to a factoring problem.)x2 – x – 20 = 0(x – 5)(x + 4) = 0(x – 5) = 0 gives x = 5, and (x + 4) = 0 gives x = -4Therefore the domain is {x | x ≠ 5 and x ≠ -4}Multiply the following rational expressions.3 2 23 3 362 2a a b a b aa a a b+ + +�+ +Example2 23:aANSWERa ab b- +Solution: Factor each polynomial completely,then cancel all factors that appear on both the top and the bottom.NOTE: This problem uses factoring by grouping, factoring out a GCF (twice!), and the sum of cubes formula. Whew!Add the following rational expressions.65,6422 xxxxx 656422xxxxx )2)(3()2)(3(4xxxxx)3)(2)(3()3()3)(2)(3()3(4xxxxxxxxx)3)(3)(2(31242xxxxxx)3)(3)(2(122xxxxxExampleDividing a polynomial by a monomialDivide each term of the polynomial separately by the monomial.aaa31536123aaaaa3153363123aa51242Example152328372 xxxx4xx 1228235 x51535  xDivide 7x into 28x2.Multiply 4x times 7x+3.Subtract 28x2 + 12x from 28x2 – 23x.Bring down -15.Divide 7x into –35x.Multiply -5 times 7x+3.Subtract –35x–15 from –35x–15.Nothing to bring down.15So our answer is 4x – 5.ExampleDividing a trinomial by a binomial:HOW WOULD YOU CHECK THIS ANSWER???Example of a complex fraction: 10 3x . 5 6xSolution: view as a division problem: 10 ÷ 5 = 10 · 6x = 4 3x 6x 3x 5Example: Solving a rational equation:Solve 2x + 1 = 1 . 2x – 1 x 2x – 1Solution: 1. Multiply both sides by the LCD x(2x – 1). This gives 2x(x) + 1(2x – 1) = 1(x)2. Now simplify this equation: 2x2 + 2x – 1 = x 2x2 + x – 1 = 03. Solve either by factoring or by using the quadratic formula. Answers: x = -1, x = 1/2Example


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