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# Polynomial Division?

Is there anyway to solve this without long division? Any shortcuts?

Update:

For this problem (w^5 - z^5) / (w-z)

### 3 Answers

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- Rita the dogLv 76 years agoFavorite Answer
The remainder theorem guarantees that there is no remainder. But I think you will have to use long division (or perhaps synthetic division). You should get: w^4 + w^3 z + w^2 z^2 + w z^3 + z^4

- moeLv 76 years ago
Note: a^5-b^5 = (a – b) (a^4 + a^3b + a^2b^2 + ab^3 + b^4 )

now,

W^5 - Z^5) / (W - Z)

= {(W – Z) (W^4 + W^3Z + W^2Z^2 + WZ^3 + Z^4 )} / (W - Z)

= (W^4 + W^3Z + W^2Z^2 + WZ^3 + Z^4 )

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