Polynomials Unit 3.3

Polynomials Unit 3.3

1. leading term: term w/ highest power-- ax^2

   • degree of a polynomial: power of x-- 2
     • # of zeros
   • Leading coefficent: coefficient-- a

2. expression when...n is an integer and n>0

   • anxn+an-1wn-1

3. Classifying by terms:

   • 1: monomial
     • 2: binomial
       • 3: trinomial
         • 4: polynomial
           • 4+: polynomial

4. Classifying by power

   • 0: constant
     • 1: linear
       • 2: quadratic
         • 3: cubic
           • 4: quartic
             • 5: quintic
               • n: nth degree

5. 4 sqrt. X--4X^(1/2)

   • Example:
   • No-- n is not an integer

6. Reminders:

   • Make sure all terms are in STANDARD FORM
   • SQRT: ^(1/2)

7. Characteristics of a Polynomial

   • are continuous...no breaks, holes, gaps
     • smooth curves
   • Local Extrema
     • Peaks and valleys have local max./min.
       • Turning points
       • Can be found manually-- halfway b/n x-int.
     • appr. to nearest thousandth
   • Increasing/Decreasing Intervals
     • Find using-- X VALUES
       • interval notation-parentheses