Question 47148
If x = -1 is a root of{{{x^3+2x^2-x-2 = 0}}}, then x+1 is a factor of this polynomial.
You can find the other factors and, hence, the other roots, by dividing the given polynomial by the factor (x+1)

{{{(x^3+2x^2-x-2)/(x+1) = x^2+x-2}}} Now factor the right side.
{{{x^2+x-2 = (x+2)(x-1)}}}

Now we have:{{{x^3+2x^2-x-2 = (x+1)(x+2)(x-1)}}} and...
{{{(x+1)(x+2)(x-1) = 0}}} Applying the zero products principle, we get:
{{{x+1 = 0}}} and {{{x = -1}}}
{{{x+2 = 0}}} and {{{x = -2}}}
{{{x-1 = 0}}} and {{{x = 1}}}