Final answer:
To find the expression equivalent to (2x³ - 15x² + 17x + 3)/(x - 5), one needs to use polynomial long division or synthetic division. The quotient will be a second-degree polynomial, as the division is by a first-degree polynomial x-5.
Step-by-step explanation:
The student is asking how to simplify the algebraic expression (2x³ - 15x² + 17x + 3)/(x - 5).
To find the equivalent expression, one must perform polynomial long division or synthetic division since there is no obvious simplification. After dividing the polynomial by x - 5, you would obtain the quotient which should be equivalent to one of the answer choices provided.
The correct process would be to list down the coefficients of the polynomial, perform the synthetic division using the root which is 5 (since we divide by x - 5), and then write down the resulting polynomial expression from the coefficients obtained from the synthetic division.
The final expression would not contain an x value with a power higher than two because you are dividing by a first-degree polynomial.