Find the value of k for which the first polynomial is a factor of the second polynomial.?

x + 4; x^3 + 6x^2 + 7x + k

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  • 4 weeks ago

    f(x) = x³ + 6x² + 7x + k

    If x + 4 is a linear factor then f(-4) = 0

    i.e. (-4)³ + 6(-4)² + 7(-4) + k = 0

    => -64 + 96 - 28 + k = 0

    Hence, k = -4

    :)>

  • 4 weeks ago

    Find the value of k for which the first polynomial is a factor of the second polynomial.?

    x + 4; x^3 + 6x^2 + 7x + k

    (x^3 + 6x^2 + 7x + k) / (x + 4)

    (x^3 + 6x^2 + 7x - 4) / (x + 4)

    x^3 + 6 x^2 + 7 x - 4 = (x^2 + 2 x - 1) × (x + 4) + 0

  • 4 weeks ago

    If x + 4 is a factor then -4 is a zero. Plug in -4 for x and choose k to make the answer zero:

    -64 + 96 - 28 + k = 0 etc

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