Question

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

Answer 1

`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`.