f(x) = 7x^3 + 8x^2 - 3x + 8

Find f(7) using synthetic division, and list the numbers in the bottom row of the division.

My answer: The numbers in the bottom row are 7, 58, 403, and 2829. The answer is 7x^2 + 58x + 403 + 2829/x - 7.

enter your coefficients at

http://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php

Looks like you goofed somewhere.

Messed up big time...

It's 7x^2 + 57x + 396 + 2780/x - 7.

To find f(7) using synthetic division, follow these steps:

1. Write down the coefficients of the polynomial in ascending order: 7, 8, -3, 8, 0.
Note: If there is a missing power of x, write a placeholder zero.

2. Set up the synthetic division table:
┌──────────┬─────────────┬──────────────┬───────────────┬─────────────┐
│ 7 │ 8 │ -3 │ 8 │ 0 │
└──────────┴─────────────┴──────────────┴───────────────┴─────────────┘

3. Bring down the first coefficient, which is 7, into the leftmost box beneath the division bar.
┌──────────┬─────────────┬──────────────┬───────────────┬─────────────┐
│ 7 │ 8 │ -3 │ 8 │ 0 │
│ │ │ │ │ │
└──────────┴─────────────┴──────────────┴───────────────┴─────────────┘

4. Multiply the divisor, 7, by the number in the current box (7) and place the result (49) in the next box.
┌──────────┬─────────────┬──────────────┬───────────────┬─────────────┐
│ 7 │ 8 │ -3 │ 8 │ 0 │
│ │ 49 │ │ │ │
└──────────┴─────────────┴──────────────┴───────────────┴─────────────┘

5. Add the numbers in the bottom row (8 + 49 = 57) and write the result in the corresponding box.
┌──────────┬─────────────┬──────────────┬───────────────┬─────────────┐
│ 7 │ 8 │ -3 │ 8 │ 0 │
│ │ 49 │ │ 57 │ │
└──────────┴─────────────┴──────────────┴───────────────┴─────────────┘

6. Multiply the divisor, 7, by the number in the current box (57) and place the result (399) in the next box.
┌──────────┬─────────────┬──────────────┬───────────────┬─────────────┐
│ 7 │ 8 │ -3 │ 8 │ 0 │
│ │ 49 │ │ 57 │ 399 │
└──────────┴─────────────┴──────────────┴───────────────┴─────────────┘

7. Add the numbers in the bottom row (-3 + 399 = 396) and write the result in the corresponding box.
┌──────────┬─────────────┬──────────────┬───────────────┬─────────────┐
│ 7 │ 8 │ -3 │ 8 │ 0 │
│ │ 49 │ 396 │ 57 │ 399 │
└──────────┴─────────────┴──────────────┴───────────────┴─────────────┘

8. Multiply the divisor, 7, by the number in the current box (396) and place the result (2772) in the next box.
┌──────────┬─────────────┬──────────────┬───────────────┬─────────────┐
│ 7 │ 8 │ -3 │ 8 │ 0 │
│ │ 49 │ 396 │ 57 │ 399 │
└──────────┴─────────────┴──────────────┴───────────────┴─────────────┘

9. Add the numbers in the bottom row (8 + 2772 = 2780) and write the result in the corresponding box.
┌──────────┬─────────────┬──────────────┬───────────────┬─────────────┐
│ 7 │ 8 │ -3 │ 8 │ 0 │
│ │ 49 │ 396 │ 57 │ 399 │
└──────────┴─────────────┴──────────────┴───────────────┴─────────────┘

10. The bottom row represents the coefficients of the quotient polynomial: 7, 58, 403, 2780.
Therefore, f(7) = 7x^3 + 58x^2 + 403x + 2780.