Final answer:
Calculators typically cannot factor complex polynomials algebraically, but theoretic methods for manual calculations include synthetic division and long division, which fall under polynomial division. Modern calculators use numerical methods instead. The use of mathematical equations in modeling linear aspects of ecosystems is called analytical modeling.
Step-by-step explanation:
When it comes to factoring complex polynomials, calculators often use numerical methods rather than algebraic ones. Typically, a calculator cannot directly factor a complex polynomial in the way a human does through algebraic manipulation. However, if we are considering a method that is algebraically used and theoretically could be implemented in a calculator's programming, then polynomial division is a possible method. Polynomial division can be executed through either synthetic division or long division, depending on the specific polynomial's characteristics and the calculator's algorithm.
Out of the options provided (synthetic division, long division, factoring by grouping, polynomial division), polynomial division encompasses both synthetic and long division and represents a broader category of methods that could be used for factoring polynomials. However, this does not typically represent how modern calculators handle complex polynomial factoring.
In the context of the reference information provided on modeling linear aspects of ecosystems, the method described is known as analytical modeling, which involves the use of mathematical equations.