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Factor Theorem problem

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Given that x^2-x-2 and x^3+kx^2-10x+6 have a common factor, find the possible values of k.

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x^2 - x - 2 = (x + 1)(x - 2) x^3 + kx^2 - 10x + 6 is divisible by (x + 1) and (x - 2): x = -1 and x + 2 makes x^3 + kx^2 - 10x + 6 equal to zero. (-1)^3 + k * (-1)^2 - 10(-1) + 6 = 0 k = -15 (2)^3 + k * (2)^2 - 10(2) + 6 = 0 k = 3/2 For k = -15 and 3/2

            
        

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