Please 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 Wing Monday through Thursday 8 00 a m 6 30 p m Review for Test 3 NOTICE 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 3 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 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 2 x 3x 4 Find the domain of the expression x 2 x 20 Solution 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 4 Therefore the domain is x x 5 and x 4 Example Multiply the following rational expressions 3 2 2 a a b a b 6a 3 3 3 a a 2a 2b Solution Factor each polynomial completely then cancel all factors that appear on both the top and the bottom 3a ANSWER 2 a ab b 2 NOTE This problem uses factoring by grouping factoring out a GCF twice and the sum of cubes formula Whew Example Add the following rational expressions 4 x 2 2 x x 6 x 5x 6 4 x 4 x 2 2 x x 6 x 5 x 6 x 3 x 2 x 3 x 2 4 x 3 x x 3 x 3 x 2 x 3 x 3 x 2 x 3 4 x 12 x 2 3 x x 2 x 12 x 2 x 3 x 3 x 2 x 3 x 3 Dividing a polynomial by a monomial Divide each term of the polynomial separately by the monomial Example 12a 3 36a 15 12a 3 36a 15 3a 3a 3a 3a 5 2 4a 12 a Example Dividing a trinomial by a binomial 4x 5 2 7 x 3 28 x 23x 15 2 28 x 12 x 35 x 15 35 x 15 Divide 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 So our answer is 4x 5 HOW WOULD YOU CHECK THIS ANSWER Example of a complex fraction 10 3x 5 6x Solution view as a division problem 10 5 10 6x 4 3x 6x 3x 5 Example Solving a rational equation Solve 2x 1 1 2x 1 x 2x 1 Solution 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 0 3 Solve either by factoring or by using the quadratic formula Answers x 1 x 1 2 Example continued NOW CHECK BOTH ANSWERS in original equation Note that when you plug in x 1 everything checks out OK you get 1 3 1 3 BUT when you plug in x 1 2 you get zeroes in some denominators so this number is NOT a solution it gives 1 1 1 0 0 So the final answer is just x 1 if you write x 1 1 2 you ll get ZERO credit Reminders Be on time so you re logged in and ready to go when I give you the password This test will take the entire 55 minute class period Bring your POWER CORD No IPODS or other devices with earphones can be used during the test so turn them off and stow …