(x^5+17x^6+16x+14)/(x^2+14) =
17x^4 + x^3 - 238x^2 - 14x + 3332
x^2 + 14 [ 17x^6 + x^5 + 0x^4 + 0 x^3 + 0x^2 + 16x + 14) ]
17x^6 + +238x^4
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x^5 - 238x^4 + 0x^3
x^5 + 14x^3
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-238x^4 - 14x^3 + 0x^2
-238x^4 -3332x^2
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-14x^3 + 3332x^2 + 16x
-14x^3 -196x
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3332x^2 + 212x + 14
3332x^2 + 46648
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212x - 46634
So...the result is 17x^4 + x^3 - 238x^2 - 14x + 3332 with R [ 212x - 46634 ] / [ x^2 + 14 ]