Question 856389
How did you find one of the values to be x=-7?  If you found this, then perform synthetic division on the given polynomial to continue looking for more roots. (Polynomial division, in case you do not yet know synthetic division).


You keep looking for roots (trying rational roots) until you have found all that you can.  Your first successful synthetic division( giving remainder of zero) will give a quotient which will have its own roots, which are also roots of the original polynomial.


-----solution method----


Synthetic Division to check x=-7:
{{{x^3-8}}} quotient.
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Synthetic Division on {{{x^3-8}}} to check for x=2:
{{{x^2+2x+4}}} quotient.
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Factorization gives {{{(x+7)(x-2)(x^2+2x+4)=0}}}.
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Using general solution to quadratic equation for roots of the quadratic factor give .... {{{x=-1-i*sqrt(3)}}} and {{{x=-1+i*sqrt(3)}}}


The equation has FOUR different solutions for x.
{{{x=-7}}}, {{{x=2}}}, {{{x=-1-i*sqrt(3)}}}, {{{x=-1+i*sqrt(3)}}}