Final answer:
To determine if a binomial is a factor of the polynomial f(x), one can use the Factor Theorem or synthetic division. If f(c)=0 for the root corresponding to the binomial (x-c), or if synthetic division yields no remainder, the binomial is a factor.
Step-by-step explanation:
The question is asking for a determination of whether a given binomial is a factor of a polynomial function ‘f(x)’. To do this, we employ either the Factor Theorem or the synthetic division method. If the Factor Theorem is used, we need to evaluate the polynomial at the root that would correspond to the binomial. Specifically, if our binomial is (x - c), we evaluate f(c). If f(c) equals zero, then the binomial is indeed a factor of f(x).
In cases where the synthetic division is used, we divide the polynomial f(x) by the binomial. If the remainder is zero, then the binomial is a factor of f(x). If a student desires to check the reasonableness of their result, they could consider if the result aligns with known values, the context of a problem, or checks the units of measure if applicable.