Question 1041569
f(x)=x^3+2x^2-x-2
Remainder theorem says that if one divides by a number a, the remainder is f(a).
We want f(a)=0
synthetic division
2|1===2===-1====-1
=1==  4====7====12; f(2)=12
-2
==1===0===-1===0
-2 is a root, so (x+2) is a factor.
The quotient is the other factor, or x^2-1, which factors into (x+1)(x-1) by difference of squares.
Set those equal to zero, and the roots are -2,-1,and 1, on the interval {-4,4}.  Those are all the values of a where f(a)=0.
{{{graph(300,300,-10,10,-10,10,x^3+2x^2-x-2)}}}