(w^{3 }- 15w - 11) ÷ (w-4)
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w - 4 / w^{3} - 15w - 11
first check your polynomial to see if it contains all powers of the variable w. If not, you must add placeholders for them using zero as the coefficient. In this case, the second power is missing so we add 0w^{2}
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w - 4 /w^{3} + 0w^{2} - 15w - 11 now we are ready to divide
the first step is w^{3} ÷ w (first term divided by first term) and you put the answer on top. Then you multiply your answer by the divisor (w - 4) and write the answer below the dividend. Then you substract. Then you bring down the next term and
add it to the new dividend. The second step is the same as the first only now you use the new dividend and divide the first term by first term. This is what it looks like.
______w^{2} + 4w + 1
w - 4 /w^{3} + 0w^{2} - 15w - 11
w - 4 /w^{3} + 0w^{2} - 15w - 11
w^{3} - 4w^{2}
4w^{2} - 15w
4w^{2} - 16w
w - 11
w - 4
-7
So the answer is w^{2} + 4w + 1 with remainder -7 or we write -7 / w - 4
To check your answer you multiply (w - 4) (w^{2} + 4w + 1 -7/(w - 4) ) and you should get the original dividend