Coming up:

1. Coming up: • Today: Section 5.4 • Next class: Section 5.6 (last new section!) • Next two class days after that: • Review for Quiz 3 • Quiz 3 on sections 5.1-5.4 and 5.6

2. Gateway Quiz Reminder! If you have not passed your gateway quiz yet, remember to come in, review the last one you took, and sign up to take the next version. After this week there are just four weeks left in the semester, including finals week.

3. Any questions on the Section 5.3 homework?

4. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials.

5. Section 5.4More on Multiplying Polynomials Review from last section: When multiplying 2 binomials, the distributive property can be easily remembered as the FOIL method. F – product of First terms O – product of Outside terms I – product of Inside terms L – product of Last terms

6. = y2 – 8y – 48 Example Multiply (y – 12)(y + 4) (y – 12)(y + 4) Product of First terms is y2 (y – 12)(y + 4) Product of Outside terms is 4y (y – 12)(y + 4) Product of Inside terms is -12y (y – 12)(y + 4) Product of Last terms is -48 F O I L y2 + 4y – 12y – 48 (y – 12)(y + 4) =

7. In the process of using the FOIL method on products of certain types of binomials, we see specific patterns that lead to special products. Examples: Squaring a Binomial • (a + b)2 = a2 + 2ab + b2 • (a – b)2 = a2 – 2ab + b2 Note: These might be just as easy to do by the usual FOIL method, which is what we will demonstrate in class, rather than by memorizing these formulas.

8. Multiply (3x + 4)2 Remember that a2 = a• a, so (3x + 4)2 = (3x + 4)(3x + 4). Example (3x + 4)2 =(3x + 4)(3x + 4) = (3x)(3x + 4) + 4(3x + 4) = 9x2 + 12x + 12x + 16 = 9x2 + 24x + 16 EXTREMELY IMPORTANT NOTE: (3x + 4)2 is NOT simply (3x)2 + 42 !!!

9. Example Multiply (5x – 2z)2 (5x – 2z)2 = (5x – 2z)(5x – 2z) = (5x)(5x – 2z) – 2z(5x – 2z) = 25x2 – 10xz – 10xz + 4z2 = 25x2 – 20xz + 4z2 REMINDER: (5x -2z)2 is NOT simply (5x)2 – (2z)2 !!!

10. Problem from today’s homework:

11. Another special products pattern is seen when multiplying the sum and difference of two terms such as (a + b)(a – b) . By the FOIL method: (a + b)(a – b) = a ∙a + a ∙(-b) + a ∙b + b ∙(-b) = a2 – ab + ab – b2 = a2 – b2 Recognizing this pattern can save you some time, since the middle terms will always cancel each other out. (a + b)(a – b) = a2 – b2

12. Problem from today’s homework:

13. Problem from today’s homework:

14. Problem from today’s homework:

15. Problem from today’s homework:

16. Reminders: Next class session: HW 5.4 due at start of class Don’t forget to take this week’s Gateway in the open lab if you haven’t yet scored 8/8. Sign up for a time with a TA in the open lab next door, or email Krystle at mayerkr@uwstout.edu.

17. Math TLC Open Lab Hours: Room 203 Jarvis Hall Science Wing (next door to the JHSW 214 Math TLC classroom) Monday through Thursday 8:00 a.m. – 7:30 p.m. This lab is closed on Fridays, on weekends and during breaks.

18. Gateway Quiz Retake Times • Mondays: • 1:25 pm • 2:30 pm • Tuesdays: • 12:20 pm • 1:25 pm • Wednesdays: • 10:10 am • 11:15 am • Thursdays: • 10:10 am • 11:15 am SIGN UP IN THE MATH TLC OPEN LAB! If NONE of the above times work for you… email Krystle Mayer, Math TLC Coordinator, (mayerkr@uwstout.edu) to set up a date and time

19. You may now OPEN your LAPTOPS and begin working on the homework assignment.