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Thread: Polynomials Question

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    Junior Member bujolover's Avatar
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    Question Polynomials Question

    P(x) is a polynomial of degree 3.
    Find P(x), given that :
    - y = P(x) is an odd function.
    - (x - 2) is a factor of P(x).
    - when P(x) is divided by (x + 4), the remainder is 96.

    I don't get how to do it, and the given solution doesn't make sense to me because the first line says to let P(x) = ax3 + bx. Shouldn't it be let P(x) = ax3 + bx2 + cx + d? How do they know that b and c are 0?

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    Senior Member jazz519's Avatar
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    Re: Polynomials Question

    Quote Originally Posted by bujolover View Post
    P(x) is a polynomial of degree 3.
    Find P(x), given that :
    - y = P(x) is an odd function.
    - (x - 2) is a factor of P(x).
    - when P(x) is divided by (x + 4), the remainder is 96.

    I don't get how to do it, and the given solution doesn't make sense to me because the first line says to let P(x) = ax3 + bx. Shouldn't it be let P(x) = ax3 + bx2 + cx + d? How do they know that b and c are 0?
    Straight off the b and c are zero because its a odd function (these can only have the odd x to the power so i.e. means like three and one and not the two and zero). This can also be proven algebraically
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