# How do you create a polynomial p which has zeros #c=1, c=3#, #c=-3# is a zero of multiplicity 2, the leading term is #-5x^3#?

##### 1 Answer

Aug 6, 2017

#### Answer:

#### Explanation:

Note that

So in order to have zeros

#(x-1)(x-3)(x+3) = (x-1)(x^2-9) = x^3-x^2-9x+9#

In order that its leading term be

#-5(x^3-x^2-9x+9) = -5x^3+5x^2+45x-45#