Katie,
When your textbook say that X^{2} + 4X + 6 is a factor of X^{4} + rX^{2} + s I think the authors mean that there are numbers a and b so that
X^{4} + rX^{2} + s = (X^{2} + 4X + 6)(X^{2} + aX + b)
Expand the right side and then the right and left sides should be identical polynomials.
Steve and Penny
