If x + 1 is a factor of p(x) = x³ + k x² + x + 6, then by the remainder theorem, we have
p (-1) = (-1)³ + k (-1)² + (-1) + 6 = 0 → k = -4
So we have
p(x) = x³ - 4x² + x + 6
Dividing p(x) by x + 1 (using whatever method you prefer) gives
p(x) / (x + 1) = x² - 5x + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
x² - 5x + 6 = (x - 3) (x - 2)
so that, in addition to x = -1, the other two zeros of p(x) are x = 3 and x = 2
