Step 1

The given polynomial is \(\displaystyle{P}{\left({x}\right)}={x}^{{{3}}}-{3}{x}^{{{2}}}-{10}{x}+{24}\) whose one of the factors is \(x=2\)

Divide the polynomial by \(x-2\).

Step 2

The quotient is \(\displaystyle{x}^{{{2}}}-{x}-{12}\).

Factorize the polynomial \(\displaystyle{x}^{{{2}}}-{x}-{12}\) and find the zeros

\(\displaystyle{x}^{{{2}}}-{x}-{12}={0}\)

\((x-4)(x+3)=0\)

\(x=4. x=-3\)

Hence, the zeros are \(x=4. x=-3\ and\ x=2.\)