How do you write a polynomial function in standard form with Zero: 5, multiplicity 3?

1 Answer
Jul 15, 2016

Answer:

#x^3-15x^2+75x-125#

Explanation:

A zero, say #a# of a polynomial #f(x)# is one for which #f(a)=0#.

Let us assume that zeros are #{a,b,c,d}#, then it is apparent that such a polynomial could be #(x-a)(x-b)(x-c)(x-d)#.

As we need to write a polynomial with zero #5# with multiplicity #3#, the polynomial is

#(x-5)^3# and using identity #(x-a)^3=x^3-3ax^2+3a^2x-a^3#, this can be expanded
as

#x^3-3×x^2×5+3×x×5^2-5^3# or

#x^3-15x^2+75x-125#.