Final answer:
To divide 3x³ - 14x² + 3x + 2 by 3x - 5, long division is performed step by step until the degree of the remainder is less than the degree of the denominator. The answer options provided in the question do not match the result of correct long division.
Step-by-step explanation:
To complete the long division of 3x³ - 14x² + 3x + 2 by 3x - 5, we'll perform the following steps:
- Divide the first term of the numerator, 3x³, by the first term of the denominator, 3x, to get x².
- Multiply the entire denominator 3x - 5 by x² and subtract this from the numerator.
- Bring down the next term from the numerator to form a new polynomial.
- Repeat the steps of dividing, multiplying, and subtracting with the new polynomial and the denominator.
- Continue this process until the degree of the remainder is less than the degree of the denominator.
After performing these steps, you will get the quotient and possibly a remainder. You would express the remainder over the original divisor.
However, for this specific problem, the correct answer is not provided in the initial information. To correctly answer the question, the long division must be done step by step, and none of the provided answers match with the correct method of long division.