The polynomial P(x) has a remainder of 2 when divided by x-1 and a remainder of 3
when divided by x-2. The remainder when P(x) is divided by (x - 1)(x-2) is ax + b,
i.e. P(x) can be written as P(x) = (x - 1)(x-2)Q(x) + ax + b.

a. Find the values of a and b.

bi. Given that P(x) is a cubic polynomial with coefficient of x3³ being 1, and -1 is a
solution of the equation P(x) = 0, find P(x).

bii. Show that the equation P(x) = 0 has no other real solutions.