Topics:

• Completing the square in order to use trig substitution. See my notes on Piazza from my WeBWorK problem which I showed on the board in class. (WeBWorK “Trigonometric Substitution 3” problems 9, 18, 21, and 3 use this. 3 is a little more challenging.)

• Back to partial fractions expansion when the denominator has only linear factors: Examples 183 and 184. I showed the details of the long division for Ex. 184, and I will try to type that up when I have time. I have not yet found any nice videos that show long division used in partial fractions except for this one from Khan Academy. If you need to review long division of polynomials, Khan academy has a number of videos on that topic (in Algebra 2, not specific to partial fractions).

We have to use long division to reduce the degree of the numerator whenever the degree of the numerator is the same as or greater than the degree of the denominator. Partial fractions only works for rational expressions where the numerator has smaller degree than the denominator.

Homework:

• Review the examples discussed in class, and review long division of polynomials as well if you feel the need!

• Do the WeBWorK: there is an additional short assignment “Partial Fractions 2” which is also due next Tuesday. PLEASE do not wait to the last minute!

Please also remember that one of the purposes of assigning WeBWorK is that, since you get immediate feedback if your answer is wrong, the intention is that you will seek help (read the book, look at the videos I linked, post a question to Piazza, talk to a classmate or tutor… etc…) AS SOON AS POSSIBLE, not waiting for the next class meeting! Not to mention that if you post a question to Piazza, you give your fellow classmates an opportunity to help (which is always a good thing) and to earn a few quiz points (which is also a good thing).

• There will be a quiz next time: the topic will be completing the square in trig substitution (see problems 18, 21 in the WeBWorK), and partial fractions used to integrate (no long division).

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!