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    How to do this question?

    Let f(x) = 7x^32 + 5x^22 + 3x^12 + x^2 . Find the remainder when f(x) is divided by x^2 + 1.

    Is there an easier method than long division. If there isnt... how do you do this by long division as i havent learn that yet
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    (Original post by Carman3)
    How to do this question?

    Let f(x) = 7x^32 + 5x^22 + 3x^12 + x^2 . Find the remainder when f(x) is divided by x^2 + 1.

    Is there an easier method than long division. If there isnt... how do you do this by long division as i havent learn that yet
    Notice that all your terms in the polynomial are integral powers of x^2.

    So, let y=x^2.

    Your polynomial now becomes f(y) = 32y^16+ ....
    And you want the remainder when it's divided by y+1

    Doable now?

    Edit: To be strictly accurate, I should say g(y) rather than f(y), since this changes the function, and we have g(x^2) =f(x)
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    If you know about complex numbers, factorize x^2+1 and use the remainder theorem.
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    (Original post by ghostwalker)
    Notice that all your terms in the polynomial are integral powers of x^2.

    So, let y=x^2.

    Your polynomial now becomes f(y) = 32y^16+ ....
    And you want the remainder when it's divided by y+1

    Doable now?
    So you would get 7y^16+5y^11+3y^6+y

    What would you do after that... factorise it? If so, how
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    (Original post by Carman3)
    So you would get 7y^16+5y^11+3y^6+y

    What would you do after that... factorise it? If so, how
    Remainder theorem.
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    (Original post by ghostwalker)
    Notice that all your terms in the polynomial are integral powers of x^2.

    So, let y=x^2.
    Our posts must have crossed - much nicer suggestion than mine. PRSOM...
 
 
 
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