Polynomials Section 1 4 Introduction Operations Polynomial What

Polynomials (Section 1 -4) *Introduction *Operations

Polynomial: What is it? n These are: ■ These are NOT:

Polynomial: What is it? n These are: Only operations on the variable are +, -, x ■ These are NOT: Has any other operation on the variable

Terms in an Expression n Number of items added or subtracted n 3 x 2 y 5 z has 1 term n 3 x 2+y 5 z has 2 terms n 3–x 2+y 5 z has 3 terms

Terms of Polynomials n 1 monomial 3 x 2 y 5 n 2 binomial 3 x 2+y 5 n 3 trinomial 3–x 2+y 5 n 4+ no special name 3 x 5– 2 x 4+5 x 3– 6 x 2+2 x

Vocabulary of Monomial 3 x 2 3 is the numerical coefficient x is the base 2 is the exponent x 2 is a power (the second power of x)

Find degrees of polynomials 5 th degree 3 rd degree

Definition of Degree The degree of a polynomial is the maximum number of variables that appear as factors in any one term.

Vocabulary of Degrees Degree 0 1 st 2 nd 3 rd 4 th 5 th 6 th + Name Constant Linear Quadratic Cubic Quartic Quintic No special name Example 13 5 x 7 x 2 5 x 3 x 4 9 x 5 3 x 17

Adding or Subtracting Terms 2 alligators + 3 alligators = 5 alligators 2 a + 3 a = 5 a

Adding or Subtracting Terms 2 alligators + 3 beavers = 2 alligators + 3 beavers 2 a + 3 b = 2 a + 3 b

Adding or Subtracting Terms 5 ducks + 3 two-headed ducks = 5 ducks + 3 two-headed ducks 5 d + 3 d 2 = 5 d + 3 d 2

Adding or Subtracting Terms 5 Coyote. Ducks + 2 Coyote. Ducks = 7 Coyote. Ducks 5 cd + 2 cd = 7 cd

Adding or Subtracting Terms 5 Coyote. Ducks + 2 Ducks = 5 Coyote. Ducks + 2 Ducks 5 cd + 2 d = 5 cd + 2 d

Adding or Subtracting Terms 5 Cub. Ducks + 2 Cub. Two-headed. Ducks = 5 Cub. Ducks + 2 Cub. Two-headed. Ducks 5 cd + 2 cd 2 = 5 cd + 2 cd 2

Multiplying Polynomials

Multiplying Polynomials