In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):
f(x) = 4x4-3x3-2x2+x-7, g(x) = x-1
We have,
f(x) = 4x4-3x3-2x2+x-7 and g(x) = x-1
Therefore, by remainder theorem when f (x) is divided by g (x) = x – 1, the remainder is equal to f (+1)
Now, f(x) = 4x4-3x3-2x2+x-7
f (1) = 4 (1)4 – 3 (1)3 – 2 (1)2 + 1 – 7
= 4 – 3 – 2 + 1 – 7
= -7
Hence, required remainder is -7.