1. Polynomials Objectives The student will be able to: 1. find the degree of a polynomial and 2. arrange the terms of a polynomial in ascending or descending order.

2. What does each prefix mean?  Mono one  Bitwo  Trithree

3. So, what is a monomial? A monomial can be a : 1.number, 2.variable, or 3. a product of one or more numbers and variables. Here are some examples: 5 y 3x2y33x2y3

4. So, what does poly mean? one or more A polynomial is a monomial or a sum/difference of monomials. Ex. 7y - 3x + 4 – This is a trinomial Important Note!! An expression is not a polynomial if there is a variable in the denominator or there are negative exponents. Ex. - This is not a polynomial

5. The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. 1)5x 2 The degree = 2 2)4a 4 b 3 c The degree = 4 + 3 + 1 = 8 3)-3 The degree is 0, why?

6. The degree of a polynomial is the largest degree of the terms. Ex. 1) 8x 2 - 2x + 7 The degrees are: 2 1 0 Which is biggest? 2 is the degree! Ex. 2) y 7 + 6y 4 + 3x 4 m 4 The degrees are: 7 4 8 Which is biggest? 8 is the degree!

7. Find the degree of x 5 – x 3 y 2 + 4 A.0 B.2 C.3 D.5 E.10 Justify your answer.

8. A polynomial is normally put in ascending or descending order of its exponents. What is ascending order? Ex. Rewrite the following polynomial in ascending order in terms of y: 12x 2 y 3 – 6x 3 y 2 + 3y – 2x What is descending order? Ex. Rewrite the following polynomial in descending order: 8x – 3x 2 + x 4 – 4

9. Write in ascending order in terms of y: x 4 – x 3 y 2 + 4xy – 2x 2 y 3 A.x 4 + 4xy – x 3 y 2 – 2x 2 y 3 B.– 2x 2 y 3 – x 3 y 2 + 4xy + x 4 C. x 4 – x 3 y 2 – 2x 2 y 3 + 4xy D. 4xy – 2x 2 y 3 – x 3 y 2 + x 4