x=1 will always be a solution to the equation x^3+3x^2+kx-k-4 = 0 as
x^3 + 3x^2 + kx -- k -- 4 = 0 is actually (x -- 1)(x^2 + 4x + 4 + k) = 0 whatever k may be.
x^3 + 3x^2 + kx -- k -- 4 = 0 is actually (x -- 1)(x^2 + 4x + 4 + k) = 0 whatever k may be.
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this can be done by synthetic division
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how did you get (x-1)(x^2+4z+4+k)? ^
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replace x with 1 and see if it is satisfied or not?