Answer:
946
Explanation:
To find just the remainder when dividing a polynomial by x-3, you could just plug in 3 into that polynomial.
If you were dividing by x+3, the remainder would just be the polynomial evaluated at x=-3.
Anyways plugging in 3 gives
7(3)^4 + 12(3)^3 + 6(3)^2 - 5(3) + 16
Just put this into your nearest calculator .
It should output 946.
You could use synthetic division or even long.
Synthetic Division.
We put 3 on outside because we are dividing by x-3.
3. | 7. 12. 6. -5. 16
| 21. 99. 315. 930
________________________
7. 33. 105. 310. 946
The remainder is the last number in the last column.
The plugging in and the synthetic division will always work when dividing by a linear expression.