Monday's Notes ...

I was out sick. However, thanks to the help of my colleagues, the students didn't miss out on the lesson.

Monday's lesson went over the last two types of factoring that we will use this semester.

Differences of two squares: This type of quadratic polynomial has two perfect square terms that are being subtracted. The factors of this type look like the conjugates that we have seen several times in the last month and a half. To make the middle (linear) term of the quadratic drop out, the factors must have had the exact same terms, but opposite signs.

a² - b² = (a - b) (a + b)

Example: Factor 16x² - 25 = (4x - 5)(4x + 5)

Factor by grouping: This method of factoring is often used when there are 4 (or more) terms in the polynomial.

1. Create groups of the terms in such a way that each grouping has a gcf.
2. From each group, factor out the gcf.
3. The remaining factors in the parenthesis must be the same to continue. Now that the parenthesis have the exact same terms, that is a gcf of both parts of our polynomial expression. Factor the parenthesis out to the front and create another parenthesis with what is left behind.

Students saw a similar problem to Step 3 in notes from last Wednesday: Factoring by Using a Greatest Common Factor, example "l".

Example: Factor 12x³ - 8x² - 18x + 12

Step 1 - Group: (12x³ - 8x²) + (-18x + 12)

Step 2 - Find GCFs in the groupsing: 4x² (3x - 2) + -6 (3x - 2)

Step 3 - Factor out the GCF Parenthesis: (3x - 2) (4x² - 6)

Homework: Finish the Handout

Remember - there will be a quiz on Thursday covering all uses of Factoring! There will also be a binomial expansion problem (from last Monday). We will have a review session Thursday morning at 7:45 am in room 4303 to prepare for this quiz.

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