急!急! F4 Polynomials q1

26.
Let Q(x) be the quotient when f(x) is divided by (x - 1)(3x - 1).

Dividend = Division * Quotient + Remainder
f(x) = (x - 1)(3x - 1)Q(x) + px + q

When f(x) is divided by x - 1, the remainder :
f(1) = -4
p(1) + q = -4
p + q = -4 ...... [1]

f(x) is divisible by 3x - 1 :
f(1/3) = 0
p(1/3) + q = 0
p + 3q = 0 ...... [2]

[2] - [1] :
2q = 4
q = 2

Put q = 1 into [2] :
p + 3(2) = 0
p = -6

Hence, p = -6 and q = 2