SOLUTION: Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 3, multiplicity: 1 Zero: 2, multiplicity: 3 Degree: 4

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 3, multiplicity: 1 Zero: 2, multiplicity: 3 Degree: 4      Log On


   

Question 1146039: Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree.
Zero: 3, multiplicity: 1
Zero: 2, multiplicity: 3
Degree: 4
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


A zero of multiplicity 1 at x=3 means one factor of (x-3);
A zero of multiplicity 3 at x=2 means three factors of (x-2).

1 factor of (x-3) and 3 factors of (x-2) makes the degree 4, so there are no other factors.

And the leading coefficients of 1 in all the factors means the leading coefficient of the polynomial is 1.

ANSWER:

f(x) = (x-3)(x-2)^3

Expand and simplify if required....