The remainder theorem in a table

The remainder theorem says that dividing $p(x)$ by $x - a$ leaves the remainder $p(a)$. You will divide by synthetic division and put the two side by side in a table.

The idea. Synthetic division: bring down the first coefficient; then, for each next coefficient, add $a$ times the last number. The last number is the remainder.

Your tasks.

1. In divide, return the pair (quotient, remainder).
2. Fill table with (a, remainder, value) for $a = -2, -1, 0, 1, 2$, for $p(x) = x^3 + 2x^2 - x + 3$.
3. Set same to True if, on every row, the remainder equals the value.