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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  • 6 years ago
    Favorite 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

  • moe
    Lv 7
    6 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 )

  • The Me
    Lv 6
    6 years ago

    It is a formula

    Attachment image
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