# Solve the equation x^3 – 5x^2 + 2x + 8

Solve the equation $$\displaystyle{x}^{{3}}–{5}{x}^{{2}}+{2}{x}+{8}={0}$$ given that -1 is a zero of $$\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}–{5}{x}^{{2}}+{2}{x}+{8}$$

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SchulzD
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 $$\displaystyle{\left\lbrace-{1}.{2}.{4}\right\rbrace}$$