When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1, we get remainders as 19 and 5 respectively.
Find the remainder if f(x) is divided by x - 3.
When f(x) is divided by (x + 1) and (x - 1), the remainders are 19 and 5 respectively.
... f(-1) = 19 and f(1) = 5
⇒ (- 1)4 - 2(- 1)3 + 3(- 1)2 - a(- 1) + b = 19
𡴡+ 2 + 3 + a + b = 19
... a + b = 13 ------------ (i)
Again, f(1) = 5
𡴡4 - 2 × 13 + 3 × 12 - a  ൱ b = 5
𡴡 - 2 + 3 - a + b = 5
... b - a = 3 ------------- (ii) 
Solving eqn (i) and (ii), we get 
a = 5 and b = 8
Now substituting the values of a and b in f(x), we get
... f(x) = x4 - 2x3 + 3x2 - 5x +8
Now f(x) is divided by (x - 3) so remainder will be f(3)
... f(x) = x4 - 2x3 + 3x2 - 5x +8
𡴯(3) = 34 - 2 × 33 + 3 × 32 - 5 × 3 + 8
          = 81 - 54 + 27 - 15 + 8 = 47
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