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16 August, 22:27

Joshua wants to know if x-5 is a factor of the polynomial P (x) = x^3-5x^2-x+5

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  1. 17 August, 00:28
    0
    See below.

    Step-by-step explanation:

    By the Factor Theorem, if (x - a) is a factor of P (x) then P (a) = 0.

    So if x - 5 is a factor then P (5) = 0:

    P (5) = 5^3 - 5 (5) ^2 - 5 + 5

    = 125 - 125 - 5 + 5

    = 0.

    Thus, x - 5 IS a factor.
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