another/better way to solve :
for above term to be -ve , either \(x^3\) or \((1-x^2)\) will be negative . Both can not have the same sign.
However there is no way to find out which one is -ve and so no way to check the sign of x
x can lie in the range -1 to 1.
either \(x^3\) or \((1-x^2)\) will be negative
x lies in the range -1 to 1 so \((1-x^2)\) can not be -ve.
Hance \(x^3\) is -ve and hance x is -ve.