In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):
f(x) = 4x3-12x2+14x-3, g(x) = 2x-1
We have,
f(x) = 4x3-12x2+14x-3 and g(x) = 2x-1
Therefore, by remainder theorem when f (x) is divided by g (x) = 2 (x - 
), the remainder is equal to f (
)
Now, f(x) = 4x3-12x2+14x-3
f (
) = 4 (
)3 – 12 (
)2 + 14 (
) – 3
= (4 * 
) – (12 * 
) + 7 – 3
= 
– 3 + 7 – 3
= 
Hence, required remainder is 
4