Question 112057
Factor:
{{{x^3+x^2-7x = 7}}} Subtract 7 from both sides.
{{{x^3+x^2-7x-7= 0}}} Factor by grouping.
{{{(x^3+x^2) - (7x+7) = 0}}} Factor {{{x^2}}} from the first group and 7 from the second group.
{{{x^2(x+1) - 7(x+1)= 0}}} Now factor the common factor of {{{(x+1)}}}
{{{(x+1)(x^2-7) = 0}}} Now apply the zero products principle.
{{{x+1 = 0}}} or {{{x^2-7 = 0}}}
If {{{x+1 = 0}}} then {{{x = -1}}}
if {{{x^2-7 = 0}}} then {{{x^2 = 7}}} so {{{x = sqrt(7)}}} or {{{x = -sqrt(7)}}}
The three roots are:
{{{x = -1}}}
{{{x = sqrt(7)}}}
{{{x = -sqrt(7)}}}