<s>[INST] The number of real roots of $x^5 + 2x^3 + x^2 + 2 = 0 $ is The number of real roots of $x^5 + 2x^3 + x^2 + 2 = 0 $ is   
A. 0;
B. 3;
C. 5;
D. 1.
I don't know how to solve this.
 [/INST] Consider the polynomial $\mod{x^3 +1} $
$x^5 + 2x^3 + x^2 + 2 \equiv -x^2 -2 + x^2 + 2 \equiv 0$
Thus, the polynomial has a factor of $x^3+1$
The remainder of the question can be done as above.
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