Divide f(x) by (x +1)

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}–{5}{x}^{{2}}+{2}{x}+{8}={\left({x}+{1}\right)}{\left({x}^{{2}}–{6}{x}+{8}\right)}\)

f(x) = 0, then

\(\displaystyle{x}^{{2}}–{6}{x}+{8}={0}\)

\(\displaystyle{\left({x}–{4}\right)}{\left({x}–{2}\right)}={0}\)

x = 2. 4

The solution is \(\displaystyle{\left\lbrace-{1}.{2}.{4}\right\rbrace}\)

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}–{5}{x}^{{2}}+{2}{x}+{8}={\left({x}+{1}\right)}{\left({x}^{{2}}–{6}{x}+{8}\right)}\)

f(x) = 0, then

\(\displaystyle{x}^{{2}}–{6}{x}+{8}={0}\)

\(\displaystyle{\left({x}–{4}\right)}{\left({x}–{2}\right)}={0}\)

x = 2. 4

The solution is \(\displaystyle{\left\lbrace-{1}.{2}.{4}\right\rbrace}\)