January 12, 2017
Rational Root Theorem and Multiplicity
or Rational Root Theorem
Example 1:
Use the Rational Root Theorem to find all POSSIBLE rational roots (p/q).
a.
b.
factors of p:
factors of p:
factors of q:
factors of q:
p/q:
p/q:
Example 2:
Find all zeros of the function.
a.
b.
January 12, 2017
Multiplicity
Passesstraight
through:
multiplicityofone
Shapeofaparabola:
multiplicityofevendegree
assumelowestevendegree
2nddegree
Generalshapeiscubic:
multiplicityisoddgreater
thanorequalto3
assumelowestodd
degree
3rddegree
Example 3:
Given the following zeros and the multiplicity of each zero, write the general equation
of the polynomial in factored form.
a. x = 7 with multiplicity of 3, x = 0 with multiplicity of 2
b. x = –3 with multiplicity of 2, x = 3 with multiplicity of 1 and
x = 6 with multiplicity of 5
January 12, 2017
Example 4:
What is the degree of the polynomial? List the zeros of the polynomial
and the multiplicity of each zero. Sketch the graph of the function;
include the y-intercept.
a.
b.
January 12, 2017
Example 5:
List the zeros of the polynomial and the multiplicity of each zero.
Write an equation of the polynomial in factored form.
b.
a.