Step 1

Zeros, roots, and x-intercepts are all names for values that make a function equal to zero.

Given, a polynomial, f(x), has a root of \(x = 3\), a zero of \(x = -2\), and an x-intercept of \(x = -1\).

Step 2

1. The equation of this polynomial in factored form would be :

\(f(x) = (x-3)(x-(-2))(x-(-1))\)

\(\displaystyle\Rightarrow{f{{\left({x}\right)}}}={\left({x}-{3}\right)}{\left({x}+{2}\right)}{\left({x}+{1}\right)}\)

2. The equation of this polynomial in standard form would be :

\(\displaystyle{f{{\left({x}\right)}}}={\left({x}-{3}\right)}{\left({x}^{{{2}}}+{3}{x}+{2}\right)}\)

\(\displaystyle\Rightarrow{f{{\left({x}\right)}}}={x}^{{{3}}}+{3}{x}^{{{2}}}+{2}{x}-{3}{x}^{{{2}}}-{9}{x}-{6}\)

\(\displaystyle\Rightarrow{f{{\left({x}\right)}}}={x}^{{{3}}}-{7}{x}-{6}\)