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Math Help - polynomial

  1. #1
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    polynomial

    could someone show me the steps to answering this question please:

    the polynomial P(x) = x^3 + 3x^2 - 2x + k has the factor of x + 1. find the remainder when P(x) is divided by x - 3

    thanks for any help
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by mark View Post
    could someone show me the steps to answering this question please:

    the polynomial P(x) = x^3 + 3x^2 - 2x + k has the factor of x + 1. find the remainder when P(x) is divided by x - 3

    thanks for any help
    By the factor theorem P(-1) = 0. Therefore k can be found.

    Then use long division to find the remainder
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by mark View Post
    could someone show me the steps to answering this question please:

    the polynomial P(x) = x^3 + 3x^2 - 2x + k has the factor of x + 1. find the remainder when P(x) is divided by x - 3

    thanks for any help
    Well, since you know that if (x-c) is a factor of some polynomial P(x), then x=c is a zero. Therefore, P(-1)=0=(-1)^3+3(-1)^3-2(-1)+k will allow you to solve for k.

    Then you must use polynomial division to find the indictated quantity.
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  4. #4
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    i understand now, but i've got another question i'm not too sure how to tackle:

    given that P(x), where P(x) = x^3 + 3x^2 + kx + 4 and k is a constant, is such that the remainder on dividing P(x) by (x - 1) is three times the remainder on dividing P(x) by (x + 1), find the value of k

    could someone show me how it done? thankyou
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