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.

Observe by trial and error that $-1$ is a root. Then,
$$x^5+2x^3+x^2+2=(x+1)(x^4-x^3+3x^2-2x+2)=(x+1)(x^4-x^3+x^2+2x^2-2x+2)=(x+1)(x^2(x^2-x+1)+2(x^2-x+1))=(x+1)(x^2+2)(x^2-x+1)$$
Thus, there is only one real root.
