What is the sum of the cube of the roots of $ x^3 + x^2 - 2x + 1=0$? I know there are roots, because if we assume the equation as a function and give -3 and 1 as $x$:
$$
(-3)^3 + (-3)^2 - 2(-3) + 1 <0
$$
$$
1^3 + 1^2 - 2(1) + 1 > 0
$$
It must have a root between $[-3,1]$. However, the root is very hard and it appeared on a high school test. How can I solve it simply?
The given options were -10, -5, 0 , 5 and 10. Note: we didn't even learn the cube root formula. The test had just logic problems and I didn't use any calculus or complicated stuff. So there must be an easier way without using cube root concepts or formulas. 

Hint: use Newton's formulas and Vieta's formulas 
https://brilliant.org/wiki/newtons-identities/
