1. Gateway Quiz Reminder! Remember: If you haven’t yet passed the Gateway Quiz, you need to review your last one with a teacher or TA in the open lab and take the Practice Gateway again so you can this week’s Gateway Quiz. Take this seriously – you can’t pass this class without a 100% score on the Gateway, and there are only 5 weeks left after this week.

2. Wednesdays –10:10 am –11:15 am Thursdays –10:10 am –11:15 pm Gateway Quiz Retake Times (One new attempt allowed per week, beginning November 2) SIGN UP IN THE MATH TLC OPEN LAB! If NONE of the above times work for you… email Krystle Mayer, Math TLC Coordinator (JHSW 201), to set up a date and time. Mondays –1:25 pm –2:30 pm Tuesdays –1:25 pm –3:35 pm

3. Any Questions on the 5.1 Homework?

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

5. Section 5.2 Polynomial vocabulary Term – a number or a product of a number and variables raised to powers Coefficient – numerical factor of a term Constant – term which is only a number A polynomial in x is a sum of terms all involving the variable x or a constant term. All the terms in a polynomial must have whole number exponents for the powers of x.

6. In the polynomial 7x 5 + x 2 y 2 – 4xy + 7 There are 4 terms: 7x 5, x 2 y 2, -4xy and 7. The coefficient of term 7x 5 is 7, The coefficient of term x 2 y 2 is 1, The coefficient of term –4xy is –4 and The coefficient of term 7 is 7. 7 is a constant term. (no variable part, like x or y)

7. A Monomial is a polynomial with 1 term. for example: 7x 2 A Binomial is a polynomial with 2 terms. for example: 10xy+15 A Trinomial is a polynomial with 3 terms. for example: x 2 +2x-3

8. Degree of a term To find the degree, take the sum of the exponents on the variables contained in the term. Degree of the term 7x 4 is 4 Degree of a constant (like 9) is 0. (Why? because you could write it as 9x 0, since x 0 = 1) Degree of the term 5a 4 b 3 c is 8 (add all of the exponents of all of the variables, 4+3+1=8, remembering that c can be written as c 1 ). Degree of a polynomial To find the degree, take the largest degree of any term of the polynomial. Degree of 9x 3 – 4x 2 + 7 is 3.

9. More examples: 1. Consider the polynomial 7x 5 + x 3 y 3 – 4xy Is it a monomial, binomial or trinomial? What is the degree of the polynomial? 2. How about the type and degree of these polynomials? 5x 4 + 10 3x + 5   y 2 + 6y – 8 7x4y3z77x4y3z7 Trinomial CAREFUL! It is 6, not 5. Binomial, Degree 4 Binomial, Degree 1 Trinomial, Degree 10 Trinomial, Degree 2 Monomial, Degree 14

10. Example from today’s homework:

11. Like terms Terms that contain exactly the same variables raised to exactly the same powers. Combine like terms to simplify. x 2 y + xy – y + 10x 2 y – 2y + xy = Only like terms can be combined through addition and subtraction. Warning! Example 11x 2 y + 2xy – 3y(1 + 10)x 2 y + (1 + 1)xy + (-1 – 2)y = (x 2 y + 10x 2 y)+ (xy + xy) – (y – 2y) = (like terms are grouped together)

12. ANSWER:

13. Adding polynomials Combine all the like terms. Subtracting polynomials Change the signs of the terms of the polynomial being subtracted, and then combine all the like terms.

14. 3a 2 – 6a + 11 Example Add or subtract each of the following, as indicated. 1) (3x – 8) + (4x 2 – 3x +3) = 4x 2 + 3x – 3x – 8 + 3 = 4x 2 – 5 2) 4 – (-y – 4) = 4 + y + 4 = y + 4 + 4= y + 8 3) (-a 2 + 1) – (a 2 – 3) + (5a 2 – 6a + 7) = -a 2 + 1 – a 2 + 3 + 5a 2 – 6a + 7 = -a 2 – a 2 + 5a 2 – 6a + 1 + 3 + 7 = = 3x – 8 + 4x 2 – 3x + 3

15. ANSWER: 2x 2 + 8

16. In the previous examples, after discarding the parentheses, we would rearrange the terms so that like terms were next to each other in the expression. You can also use a vertical format in arranging your problem, so that like terms are aligned with each other vertically.

17. An example of “vertical” subtraction

18. Back in Chapter 1 we saw problems like this: “Subtract − 4 from 10.” In these problems we would find 10 −(-4)=10+4=14. We can do the same with polynomials: Subtract (24x 2 +11) from (61x 2 +6). This would mean we need to take: 61x 2 +6−(24x 2 +11)= 61x 2 +6 − 24x 2 -11= 37x 2 − 5

19. Evaluating a polynomial for a particular value involves replacing the value for the variable(s) involved. Find the value of 2x 3 – 3x + 4 when x = -2. Example = 2(-2) 3 – 3(-2) + 42x 3 – 3x + 4 = 2(-8) + 6 + 4 = − 6

20. (b) answer: − 25

21. Another example from today’s homework. All we need to realize here is that we are given the time, t, and need to substitute it into our given polynomial. So -16t 2 +1180= -16(1) 2 +1180=-16+1180=

22. Remember perimeter is just the sum of all the lengths of the sides. -3x 2 + 14x - 3

23. Reminder: This homework on Section 5.2 is due before the start of the next class period.

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