Answer: 3x + 2
P(x) = 6x³ + kx² - x+ 6
= 6x³ - 6x² + (k + 6)x² - (k+ 6)x + (k+5)x - (k + 5) + k + 11
= 6x²(x - 1) + (k + 6)x(x - 1) + (k+5)(x -1) + k + 11
= (6x² + (k + 6)x + k + 5)(x - 1) + k + 11
because when P(x) is divided by x - 1, the remainder is 0
=> k + 11 = 0
⇔ k = -11
with k = -11 => P(x) = (6x² - 5x - 6)(x - 1)
⇔ P(x) = (2x - 3)(3x + 2)(x - 1)
Step-by-step explanation:
