Final answer:
To divide (3x^2 - 5x - 2) by (x - 2) using long division, we would get a quotient of 3x + 1 after performing the standard division steps including dividing, multiplying, and subtracting until all terms are accounted for.
Step-by-step explanation:
To find the quotient of (3x^2 - 5x - 2) divided by (x - 2) using long division, follow these steps:
- Divide the first term of the numerator by the first term of the denominator: 3x^2 divided by x is 3x.
- Multiply the entire denominator by this result (3x) and subtract it from the numerator.
- Bring down the next term from the numerator and repeat the process until all terms are accounted for.
The expected result would be one of the answer options provided: a) 2x - 1, b) 2x + 1, c) 3x - 1, or d) 3x + 1.
When we carry out the division, we get 3x for the first term of the quotient. Multiplying (x - 2) by 3x gives us 3x^2 - 6x, which we subtract from 3x^2 - 5x. This leaves us with x. Dividing x by x gives 1, and the process ends as there are no more terms to bring down.
The final quotient is 3x + 1.