If x – 2 is a factor of the polynomial p(x) = x³ – 5x² + kx + 4, then find the value of k.​

Question

If x – 2 is a factor of the polynomial p(x) = x³ – 5x² + kx + 4, then find the value of k.​

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Amaya 2 weeks 2021-10-14T11:18:24+00:00 1 Answer 0 views 0

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    2021-10-14T11:19:51+00:00

    Answer:

    k=4

    Step-by-step explanation:

    if (x-2) is factor of polynomial, then

    x-2=0 => x = 2

    therefore for x=2 p(2) should be zero

    p(x) = x³-5x²+Kx+4

    p(2) = (2)³ – 5(2²) + 2k +4

    0 = 8 -5(4) +2k + 4

    => 0 = 8-20+4+2k

    => 2k = 8

    => k = 4

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