Consider the quotient,

f(x)/x-h
What is the remainder of this quotient?
My answer- f(x-h)

Not quite. The Remainder Theorem shows that it is f(h)

Better read it again.

To determine the remainder of the quotient, f(x)/(x-h), we can use synthetic division or perform long division.

1. Synthetic Division Method:
To use synthetic division, we need to know the value of h. Let's assume you know the value of h.

Step 1: Set up the synthetic division table with the divisor (x-h) and the dividend f(x), where the coefficients of f(x) are written in descending order of powers of x (e.g., f(x) = ax^2 + bx + c).

| h |
______________|_______|
f(x) | a | b | c |
________________|_______|
r | |

Step 2: Perform the synthetic division by bringing down the coefficients and multiplying them by h, then adding them to the next coefficient.

For example, if f(x) = 2x^2 - 5x + 3 and h = 2:
- Multiply each coefficient by 2 and write the result in the next row.
- Add each result to the respective coefficient of f(x).

| 2 |
______________|_______|
2x^2 - 5x + 3 | 2 | -10 | 6 |
________________|_______|
| 2 | -3 |

Step 3: The last number in the bottom row is the remainder. In this case, the remainder is -3.

Therefore, the remainder of f(x)/(x-h) is -3 using synthetic division.

2. Long Division Method:
If you prefer long division, you can divide f(x) by (x-h) in the same way you would divide numbers.

Step 1: Write f(x) as a long division problem, with f(x) as the dividend and (x-h) as the divisor.

____________________________
(x-h) | f(x)

Step 2: Divide the first term of f(x) (highest power of x) by the first term of (x-h). Write the result above the division line.

Step 3: Multiply the divisor (x-h) by the result obtained in Step 2 and write the product below the line. Subtract the result from the corresponding terms of f(x). Bring down the next term.

Step 4: Repeat the process of dividing, multiplying, and subtracting until there are no more terms to bring down.

Step 5: The remainder is the constant term obtained at the end of the division process.

Please provide the specific function, f(x), and the value of h to perform the long division.