Topic 1.5 Goals:

  1. Be able to determine the multiplicity of zeros of polynomials from their functions
  2. Be able to determine the degree of a polynomial from its function 
  3. Be able to determine the minimum degree of a polynomial based on given roots, including complex roots
  4. Be able to factor polynomials
  5. Be able to state missing conjugate imaginary roots
  6. Be able to state polynomial based on its real and complex roots  
  7. Be able to determine the degree of a polynomial from a table of points that lie on the graph of polynomial
  8. Know when common differences can be used to classify the degree of a polynomial
  9. Be able to use common difference to determine the degree of a polynomial
  10. Be able to use technology to perform regression on tables of points to determine coefficients and constants of related functions
  11. Be able to define a polynomial as even or odd based on its graph or related coordinates

1.5 Passwater Notes

1.5A Passwater Worksheet

Questions 1-8 correspond to determination of degree and multiplicity of zeros

Passwater Worksheet 1.5A#1

​Passwater Worksheet 1.5A#2

Passwater Worksheet 1.5A#3

Passwater Worksheet 1.5A#4

​Passwater Worksheet 1.5A#5

​Passwater Worksheet 1.5A#6

Passwater Worksheet 1.5A#7

m(x) is a quartic polynomial (4th degree)
m(x) has a point of inflection at x = -1
The root x = -1 has a multiplicity of 3
m(x) has a root at x = 1 and x = -1

Passwater Worksheet 1.5A#8

Questions 9-14 correspond to determination of missing conjugate roots

Passwater 1.5A #9

Given Complex Root x = 3 - 2i  implies x = 3 + 2i is the missing complex root
Given complex root a = 3 b = -2

Passwater 1.5A #10

Passwater 1.5A #11

Passwater 1.5A #12

Passwater 1.5A #13

Passwater 1.5A #14