Final answer:
In order to find f(3), we can use synthetic division to divide the coefficients of the polynomial function by the factor (x - 3) and find the remainder. The remainder represents the value of 71. So, none of the given options are correct.
Explanation:.
To determine the value of f(3), synthetic division proves to be a valuable method.
Begin by arranging the coefficients of the polynomial function in a row, excluding the highest degree term and placing the constant term last.
For instance, if the coefficients are 15, -36, and 11, and the goal is to evaluate f(3), utilize synthetic division with the divisor (x - 3).
Perform division for each term by 3, with the remainder written on the right side.
The process results in the following representation: 15 | -36 11, where the divisor (x - 3) is reflected in the coefficients.
Synthetic division then unfolds, producing a remainder of 71 on the right side.
Consequently, f(3) equals 71, as indicated by the remainder obtained through the synthetic division process.
This approach facilitates the efficient evaluation of polynomial functions at specific values like f(3).
Therefore, none of the given options are correct.