Question 145560
Solve for x:
{{{x^3-5x^2-x+5 = 0}}} Factor the left side.
{{{(x^2-1)(x-5) = 0}}} Appply the zero product rule: If{{{a*b = 0}}} then{{{a = 0}}} or {{{b = 0}}} or both.
{{{x^2-1 = 0}}} or {{{x-5 = 0}}}
If {{{x^2-1 = 0}}} then {{{x^2 = 1}}} and {{{x = 1}}} or {{{x = -1}}}
If {{{x-5 = 0}}} then {{{x = 5}}}
The solutions are:
{{{x = 1}}}
{{{x = -1}}}
{{{x = 5}}}