Factor Theorem-2

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Find the remainder when f(x) = x³ - 6x² + 2x - 4 is divisible by 1 - 3x.

Solution: By remainder theorem, when f(x) is divisible by 1 - 3x, the remainder = f(1/3)

f(1/3) = (1/3)³ - 6 X (1/3)² + 2 X 1/3 - 4

= 1/27 - 6/9 + 2/3 - 4

= 1/27 - 2/3 + 2/3 - 4 = (1 - 4 X 27)/27 = (1 - 108)/27 = - 107/27

Therefore, the required number is - 107 /27