Answer: C. (10n+3)
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Explanation:
We can use synthetic division.
The coefficients of [tex]10n^2-37n-12[/tex] are placed along the top, as shown in the image attachment I'm posting (see below). To the left of these three values, we have the test root 4. This is from n-4 = 0 solving to n = 4.
Follow the process of synthetic division to end up with the image attachment. We have the remainder 0 in the bottom right corner. Everything else in that bottom row will form a coefficient for the quotient, which in this case is 10n+3
If you were to multiply out (10n+3) and (n-4), you should get 10n^2-37n-12 again
(10n+3)(n-4)
10n(n-4) + 3(n-4)
10n^2-40n + 3n - 12
10n^2 - 37n - 12
The answer is confirmed.
