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14 August, 19:58

P (x) = 3 (x^2 + 10x + 5) - 5 (x - k) in the polynomial p (x) defined above, k is a constant. if p (x) is divisible by x, what is the value of k?

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  1. 14 August, 20:21
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    We have the following polynomial:

    P (x) = 3 (x ^ 2 + 10x + 5) - 5 (x - k)

    Let's rewrite the polynomial:

    P (x) = 3x ^ 2 + 30x + 15 - 5x + 5k

    P (x) = 3x ^ 2 + 25x + 15 + 5k

    For the polynomial to be divisible by x, then the constant term must be equal to zero:

    15 + 5k = 0

    Clearing k:

    5k = - 15

    k = - 15 / 5

    k = - 3

    Answer:

    the value of k is:

    k = - 3
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