dividing a polynomial by a polynomial

(-6v^2 - 4 + 9v +v^3)/ (v - 4)i am just a little lost can someone explain this to me. thanks.

Arrange the polonomial in descending order...
v^3-6v^2 +9v -4

Then divide.
v-4 !v^3-6v^2 +9v -4

The first term is v^2, so v^2*(v-4) is
subtracting that from the polonomial gives
v-4 ! -2v^2+9v-4
so dividing one gets -2v, then multiplying by v-4 gives
-2v(v-4)=-2v^2+8v, and subtracting that frm -2v^2+9v-4 gives
v-4 ! v-4, and dividing gives 1.
so the answer is v^2 -2v +1

check my thinking.

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