Month: February 2024 (Page 1 of 4)

Announcements

WebWork schedule:

• Polynomials-Divide Polynomials – due Thurs Feb 29 (Sec 1.2.5)
• Rational Expressions-Simplifying – due Fri March 1 (Sec 1.3.2)
• RationalExpressions-Multiplying and Dividing – due Mon March 4 (also Sec 1.3.2)
• Rational Expressions-Adding and Subtracting Part 1 – due Mon March 4 (Sec 1.3.3)

We will have our first midterm exam next Wed (March 6). On Monday I will discuss the topics that will be covered on the exam, and provide a list of review exercises. In the meantime, please work on the WebWork sets listed above, since the best preparation for the exam is to do the homework exercises.

Topics

We went through some more examples of multiplying/dividing and simplifying rational expressions–again, the strategy is to factor the polynomials in the numerator and denominator and then cancel common factors:

We went through the last exercise of the “RationalExpressions-Multiplying and Dividing” WebWork, which involved factoring “difference of two squares”:

We then moved on to adding and subtracting rational expressions. We started with exercises in “Rational Expressions-Adding and Subtracting Part 1” where the given rational expressions already have the same denominator, in which case we can just add/subtract the numerators (i.e., “across the top”). But in these exercises, we still need to simplify by factoring and cancelling common factors:

Next time, we will look at adding/subtracting rational expressions which don’t have the same denominator, in which case we will need to find the least common denominator (LCD), and transform the given rational expressions so they each have the LCD.

The exam will include the material we will cover in class on Monday!

Announcements

WebWork schedule:

• Polynomials-Factor Trinomials AC Method – due Tues Feb 27 (Sec 1.2.7)
• Polynomials-Divide Polynomials – due Thurs Feb 29 (Sec 1.2.5)
• Rational Expressions-Simplifying – due Thurs Feb 29 (Sec 1.3.2)
• Expressions-Multiplying and Dividing – due Mon March 4 (also Sec 1.3.2)

We will have a quiz this Wed (Feb 28), which will cover factoring polynomials, including the ac-method (i.e., the material we covered last week).

Topics

We continued with simplifying rational expressions–applying the strategy of factoring the polynomials in the numerator and denominator and then cancelling common factors:

For the example above, we introduced one of the special products–factoring a “difference of two squares”:

We then moved on to multiplying and dividing rational expressions–for which we use the same strategy of factoring and cancelling common factors. We started with a quick review of multiplying and dividing rational numbers:

We went through an example from the textbook:

We also went through some examples from the WebWork:

For dividing, we use “keep-change-flip”:

As you can see, the key to all these exercises is being able to factor polynomials!

Announcements

WebWork schedule:

• Polynomials-GCF and Factor by Grouping – due Mon Feb 26 (Sec 1.2.6)
• Polynomials-Factor Trinomials AC Method – due Tues Feb 27 (Sec 1.2.7)
• Polynomials-Divide Polynomials – due Thurs Feb 29 (Sec 1.2.5)
• Rational Expressions-Simplifying – due Thurs Feb 29 (Sec 1.3.2)

We will have a quiz this Wed (Feb 28), which will cover factoring polynomials (i.e., the material we covered this past week).

Topics

We went through the “ac-method” for factoring trinomials, in particular quadratic polynomials–the strategy is to find two numbers which multiply to ac and also sum to b:

Examples from WebWork, starting with the simplest case, where a=1 and b and c are both positive (we went through this first exercise at the end of the previous class as well):

We then went through an example where b < 0 but c > 0; in that case we know the two numbers we need for factoring are both negative (since they have to multiply to a positive c but add up to a negative b):

Then we went through an example where c < 0; then one of the numbers will be positive and one negative:

We discussed how, in the cases above, where a = 1, it’s not really necessary to do the factoring by grouping–once you identify the two numbers which multiply to ac = c and sum to b, you can jump immediately to the factorization.

But #5-9 from the WW set are cases where a > 1 — then you do have to go through the steps of “splitting the linear term” and factoring by grouping:

We then went quickly through some examples from the “Divide Polynomials” and “Rational Expressions-Simplifying” WebWorks:

Note that the last two exercises in “Polynomials-Divide Polynomials” introduce long division of polynomials. We will go through one of those examples this week but those two exercises will count as extra credit.