Each equation below is a characteristic equation for a recurrence relation. Express the solution to each recurrence relation as a linear combination of terms. Note that you will not know the actual coefficients in the linear combination since you are not given the base cases, so you can use a1, a2, etc.

(a) (x 1)(x + 2) = 0

(b) (x 4)(x 4) = 0

(c) (x 4)(x 4)(x + 5) = 0

(d) (x 4)(x 4)(x + 5)^4 = 0