What value of k makes the factor (x - 3) a factor of the function f(x)=3x^3-10x^2+x+k. ?

Answer 1

Using synthetic division

3 -10 1 k |3

9 -3 -6

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3 -1 -2 k-6

k-6 must equal 0, therefore k = 6

Answer 2

k=-12 makes

(x-3)(3x^2-x+4) = 3x^3 -10x^2 + x -12

use long division, dividing x-3 into the cubic polynomial and you'll get at the last step k--12 which would be zero if k = -12