Definition of the Fundamental Theorem of Algebra I just started learning Algebra 2, and came across the Fundamental Theorem of Algebra.
Here is how my Textbook defines it:
Every Single-Variable Polynomial Function of Degree $n \ge 1$ has at least one zero in the the set of complex numbers.
I cannot really comprehend this rule.
Take, for example, the polynomial $f(x) = x^2 + 3x + 2$
When factored, we get $(x + 2)(x + 1)$
The roots are $ x = -1, -2 $
There are no complex roots in this equation. Doesn't that disprove the Fundamental Theorem of Algebra?
 A: Recall that a complex number is a number of the form $a+bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit ($i^2=-1$). Real numbers, as mentioned in the comments, are complex numbers with $b=0$. You have two real roots, and since real numbers are part of the complex numbers, you therefore have two complex roots, and the theorem holds.
A: In the same way that natural numbers are also integers, integers are also rational numbers, and rational numbers are also real numbers, real numbers are also complex numbers (with imaginary part zero). So $x^2+3x+2$ does have two real roots (indeed, it has two integer roots); but this does not mean that it has doesn't have two complex roots.
If you want a describe a complex number that is not a real number, the correct term is non-real.* However, sometimes people use "complex number" to mean "non-real number", which is what led to your question in the first place.

*If you want to be super-precise, you should say non-real and complex, but usually there is no need to be so explicit.
