In each of the following, using the remainder theorem, find the remain

1.	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
Answer» 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.

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

Answer»

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.