Final answer:
The question involves dividing a given polynomial by (x-6), and the answer must be presented either as a polynomial p(x) or in the form p(x) + (k)/(x+5). The division process, which includes long division or synthetic division, simplifies the polynomial and checks the correctness.
Step-by-step explanation:
The question asks to divide the polynomial (2x³-13x²+9x-16)/(x-6). This division can be performed using either polynomial long division or synthetic division. It is crucial to ensure that all terms are in descending order of power and that no terms are missing, even if they have a coefficient of zero. Should there be any missing degrees, a term with a zero coefficient must be included to maintain proper alignment during division.
The process of division will provide a quotient, which is a polynomial p(x), and possibly a remainder. If there is a remainder, it should be represented in the form of k/(x+5), where k is an integer. Throughout the division process, it is essential to eliminate terms whenever possible to simplify the algebra and to check the answer to ensure its reasonableness.