Please pass your Sec. 6.6 homework worksheets to the center aisle to be picked up.

1. Please pass your Sec. 6.6 homework worksheets to the center aisle to be picked up. Any questions on the 6.6 homework problems?

2. Math TLC Open Lab Hours: Room 203 Jarvis Hall Science Wing Monday through Thursday 8:00 a.m. – 7:30 p.m. _______________________________________________________________________________________________________________

3. Review for Test 3

4. 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.

5. 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.)

6. 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.

7. 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).

8. Another goodstudy 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.)

9. 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.

10. REVIEW: Strategy for Factoring a Polynomial: • Always look first to see if there is a common factor. If so, factor out the GCF. • Determine the number of terms in the polynomial and try factoring as follows: • 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!) • 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. • 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.

11. 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.

12. Domain example: Find the domain of the expression 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}

13. Example Multiply the following rational expressions. 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!

14. Example Add the following rational expressions.

15. Example Dividing a polynomial by a monomial Divide each term of the polynomial separately by the monomial.

16. Example - 35 x - 15 Dividing a trinomial by a binomial: 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???

17. Example of a complex fraction: 10 3x . 5 6x Solution: view as a division problem: 10÷ 5 = 10 · 6x = 4 3x 6x 3x 5

18. 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

19. Example (continued): NOW CHECKBOTH 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 ½ 0 So the final answer is just x = -1 (if you write x = -1, 1/2, you’ll get ZERO credit.)

20. 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 them away before you log in to start the test.

21. Do any of you who have already started the practice test have any questions you’d like to have explained?

22. If there’s time left, go ahead and start the practice test, and we’ll come around to help if you have questions. You’re welcome to stay after class and finish your practice test in the open lab. Remember to make use of the open lab if you have any questions on the practice test problems.

23. Math TLC Open Lab Hours: Room 203 Jarvis Hall Science Wing Monday through Thursday 8:00 a.m. – 7:30 p.m. _______________________________________________________________________________________________________________