Math help please! 10 points for best fast answer! :D?

Given that (x-1) and (x+2) are factors of the expression 3x^3 + hx^2 - kx - 10. Find the values of h and k. Also find the remainder when the expression is divided by (3x-1).

Please explain what it means 'cause I'm totally lost.

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  • 9 years ago
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    The remainder theorem tells you that evaluating the polynomial at x = 1 and x = -2 will each give zero.

    So substitute each value for x in the original function to make two equations equal to zero:

    3(1)^3 + h(1)^2 - k(1) - 10 = 0

    3(-2)^3 + h(-2)^2 - k(-2) - 10 = 0

    Simplify:

    h - k = 7

    4h + 2k = 34

    Solve these two equations simultaneously:

    h = 8, k = 1

    Checking:

    3x^3 + 8x^2 - x - 10 = (x - 1) (x + 2) (3x + 5)

    (3x^3 + 8x^2 - x - 10) / (3x-1) = x^2 + 3x + (2/3) with remainder -28/3

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