Form a polynomial function of degree 5 that has a zero at x

Form a polynomial function of degree 5 that has a zero at x = -1 with multiplicity 3; a zero at x = 0; and a zero at x = 2.

Solution

Here we are given zeros at x = -1 so we get (x+1)

and multiplicty 3 so we have (x+1)^3

zeros at x= 2 so we get (x-2)

and zeros at x= 0 so we get x

On combining all ,

we get the polynomial as (x+1)^3 (x) (x-2)

This is the required polynomial of degree 5