1. Warm-up Nov. 15 Lovely quiz day! Remember that you only have 15 minutes. Good luck! HW #5: red text pg. 149 #s 15, 18, & 31 - 51 (1 st column) use pp. 9 & 10

2. Notes #3: Combining Polynomials HW #5: red text pg. 149 #s 15, 18, & 31 - 51 (1 st column) use pp. 9 & 10

3. Monomials - a number, a variable, or a product of a number and one or more variables. 4x, 20x 2 yw 3, -3, a 2 b 3, and 3yz are all monomials. Polynomials – one or more monomials added or subtracted 4x + 6x 2, 20xy - 4, and 3a 2 - 5a + 4 are all polynomials. Vocabulary

4. Binomial : a polynomial with two terms, such as ex1. 3x + 4 ex2. 5m 2 + 6m Trinomial: a polynomial with three terms, such as ex3. 5c 2 + 4c – 1 ex4. -12xy + 3y + 9 Constant: any term that doesn’t have a variable in it. Like terms: t erms with the same base 1 st term 2nd term constant 1st term 2nd term 3rd term constant

5. How do you remember the names? Think cycles! There are special names for polynomials with 1, 2 or 3 terms: 3xy 2 Monomial (1 term) 5x – 1 Binomial (2 terms) 3x + 5y 2 – 3 Trinomial (3 terms) bicycle tricycle Monocycle or Unicycle

6. Like Terms Like Terms refers to monomials that have the same variable(s) but may have different coefficients. The variables in the terms must have the same powers. Which terms are like? 3a 2 b, 4ab 2, 3ab, -5ab 2 4ab 2 and -5ab 2 are like. Even though the others have the same variables, the exponents are not the same. 3a 2 b = 3aab, which is different from 4ab 2 = 4abb.

7. Add: (x 2 + 3x + 1) + (4x 2 + 5) Add the coefficients of like terms, do not change the powers of the variables: Adding Polynomials 4x 2 + 5 Example 1: x 2 + 3x + 1 5x 2 + 3x + 6

8. Adding Polynomials Ex. 2 Add these polynomials: (2a 2 + 3ab + 4b 2 ) + (7a 2 + ab – 2b 2 ) 2a 2 + 3ab + 4b 2 7a 2 + ab – 2b 2 9a 2 + 4ab + 2b 2

9. 3.) Add: (12a 3 – 12a – 3) + (14a 3 + 16a + 4) 26a 3 + 4a + 1 12a 3 – 12a – 3 14a 3 + 16a + 4 +

10. Subtract: (3x 2 + 2x + 7) – (x 2 + x + 4) Subtracting Polynomials When subtracting polynomials, Change the signs of the second polynomial. Remember to place a 1 in front of a variable without a coefficient. 1 st polynomial2 nd polynomial Example 4: 3x 2 + 2x + 7 1x 2 + 1x + 4 2x 2 + x + 3

11. 5.) Subtract: (5x 2 – 4) – (2x 2 + 3) Steps: 1.Line up the like terms together. 2.Change the signs of the second polynomial. 3.Combine like terms Steps: 1.Line up the like terms together. 2.Change the signs of the second polynomial. 3.Combine like terms 1 st polynomial 2 nd polynomial 5x 2 – 4 -2x 2 – 3 3x 2 – 7

12. 6.) Subtract: (-4x 2 – 3x + 6) – (3x 2 + 4x – 3) Change the signs of the 2 nd poly -7x 2 – 7x + 9 -4x 2 – 3x + 6 -3x 2 – 4x + 3

13. Subtract (3b 2 + 5b + 2) from (8b 2 + 4b – 6). 8b 2 + 4b – 6 -3b 2 – 5b – 2 5b 2 – b – 8 Exit Question