## 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.