Question

Write a polynomial function with the realzeros -3, 0, and 3.

Answer 1

Recall that we can factorize any polynomial as:

$P(x)=k(x-a)(x-b)...(x-n),$

where k is a constant and a,b,...n are the root of the polynomial.

Therefore, a polynomial function with the real zeros -3,0, and 3 is:

$f(x)=k(x-3)(x-0)(x+3).$

k can be any constant, therefore, we can set k=1.

Answer:

$f(x)=x(x+3)(x-3).$