Answer:
a)
Step-by-step explanation:
the polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial x-r is equal to f(r). In particular, x-r is a divisor of f(x), if and only if f(r)=0.
our r here is 1 as the factor is x-1.
so, f(1) has to be 0.
0 = 1³ - 6×1² + k×1 - 6 = 1 - 6 + k - 6 = -11 + k
k = 11
