Maybe I shouldn't have started this blog now, not with everything that's been going on.

Last Tuesday in my Mathematical Methods 1 class I asked them to pass their assignment, which is the same as their quiz last time, since I knew that most (if not all) of them didn’t finish it.

No one passed it at the start of the class though. One of the more responsible students even said that the assignment was too difficult. But wasn’t that supposed to be the point? They had the chance to redeem themselves for not being able to answer those questions correctly (I assumed) in the test.

Anyway, another reason why I did that was because there were no classes last Monday, so we were one session short this week. Reviewing the answers to the quiz would take up too much time and then we would have to rush to finish the coverage for this Friday’s quiz.

Of course, if they had thought about it, they would have requested to review the test, and continue with the new topic at the regular pace so that there would be less topics in the next quiz. No one thought of that or voiced it out loud though.

The new topic was the remainder theorem, the factor theorem and synthetic division, which is all about division of polynomials, or rational expression of polynomials where the degree of the numerator is greater than the degree of the denominator.

Of all three, synthetic division is of course the most beneficial instead of doing long division, except that some students found it a bit confusing. I told them that for the next quiz anyway they could decide which method they wanted to use to get the remainder or to determine if a polynomial of degree one is a factor of another of greater degree.

Second most beneficial for me though was the factor theorem, because it would be easy to find out whether a two term polynomial of degree one is a factor of a larger one. This helps very much in factoring large polynomials, which figured greatly in our next topic.

This time even one of the students who had taken the subject more than once expressed appreciation for the topic. And another, who arrived in class just in time for the exercise, was still able to answer just based on the samples written on the board. This, by the way, was the only guy who passed the assignment I gave last week.

I thought I had to start on partial fractions, the next topic, because of what I had talked about with David before that arithmetic sequences and series would be part of the topics for the tenth week of classes. But the students begged against it, and in fact when I asked David afterwards what he was able to discuss in class, he said he would only start on partial fractions the next meeting, just like me.

And so that’s what I taught them on Thursday. Partial fractions are unlike the previous topic, because these involve polynomials in rational expressions where the degree of the numerator is less than the degree of the denominator. These are all in one variable, of course.

There were four subtopics here: non repeating factors of degree one, repeating factors of degree one, non repeating quadratic (or degree two) factors, and repeating quadratic factors.

We concentrated on the first three. In fact I gave an example for the second instance that had five partial fractions, and thus we had to compute for five numbers in their numerators. I assured them though that we would not have more than four variables in the quiz.

I’ll have to stop here for now. More weekend preparations beckon.

I’m not sure if I’ll be able to post tomorrow. Even though the office will be open, I don’t know if I’ll have time to pass by here in the morning or if I’ll decide instead to go straight to the venue of the field trip of my mechanics class. My next post might be on Monday.

Either way I’ll continue talking about this week’s classes then.