To be clear, it's better to state over which ring the polynomial is defined.
A polynomial in $X$ over a ring $R$ is defined as $\sum\limits_{k = 0}^n = a_kX^K$, where $a_k \in R$ for $k \in \{0,\dots,n\}$.
In particular, a polynomial over $\Bbb{R}$ admits only real coefficients, whereas a polynomial over $\Bbb{C}$ admits complex coefficients.
Remarks: For pedagogical reasons, when one find roots (of polynomials) in algebra-precalculus, one usually focus on real roots and discard the complex ones, especially in exercises of quadratic-equation. I guess it's a possible reason that your College Algebra book only consider polynomials with real coefficients. Things will become clearer when you move on to abstract-algebra.