Use synthetic division to divide. \[ \frac{7 x^{3}-63 x^{2}+62 x-48}{x-8} \]

Step 1 ：Given the polynomial \(7x^{3}-63x^{2}+62x-48\) and the divisor \(x-8\), we are to perform synthetic division.

Step 2 ：First, write down the coefficients of the dividend polynomial, which are [7, -63, 62, -48].

Step 3 ：Next, write down the value of 'a' from the divisor polynomial \(x - a\), which is 8 in this case.

Step 4 ：Bring down the first coefficient to the bottom row, which is 7.

Step 5 ：Multiply 'a' by the value just written on the bottom row, and write the result under the next coefficient. Repeat this step until all coefficients have been processed.

Step 6 ：The bottom row of numbers represents the coefficients of the quotient polynomial, and the last number is the remainder.

Step 7 ：After performing synthetic division, the coefficients of the quotient polynomial are 7, -7, and 6, and the remainder is 0.

Step 8 ：This means that the original polynomial is exactly divisible by \(x - 8\), and the quotient is \(7x^{2} - 7x + 6\).

Step 9 ：Final Answer: The quotient is \(\boxed{7x^{2}-7x+6}\) and the remainder is \(\boxed{0}\).