If c is a zero of a polynomial, then x−c is a linear factor of this polynomial.

Given the zeros −6, 6, and 0, we can write:

\(\displaystyle{f{{\left({x}\right)}}}={a}{\left({x}+{6}\right)}{\left({x}−{6}\right)}{\left({x}\right)}\)

Expand:

\(\displaystyle{f{{\left({x}\right)}}}={a}{\left({x}^{{{2}}}−{36}\right)}{\left({x}\right)}\)

\(\displaystyle{f{{\left({x}\right)}}}={a}{\left({x}^{{{3}}}−{36}{x}\right)}\) Since the leading coefficient is equal to 1, we simply let a=1:

\(\displaystyle{f{{\left({x}\right)}}}={1}{\left({x}^{{{3}}}−{36}{x}\right)}\)

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}−{36}{x}\)

Given the zeros −6, 6, and 0, we can write:

\(\displaystyle{f{{\left({x}\right)}}}={a}{\left({x}+{6}\right)}{\left({x}−{6}\right)}{\left({x}\right)}\)

Expand:

\(\displaystyle{f{{\left({x}\right)}}}={a}{\left({x}^{{{2}}}−{36}\right)}{\left({x}\right)}\)

\(\displaystyle{f{{\left({x}\right)}}}={a}{\left({x}^{{{3}}}−{36}{x}\right)}\) Since the leading coefficient is equal to 1, we simply let a=1:

\(\displaystyle{f{{\left({x}\right)}}}={1}{\left({x}^{{{3}}}−{36}{x}\right)}\)

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}−{36}{x}\)