Question

If x⁵¹+51 is divide by x+1, the remainder is
A. 0
B. 1
C. 49
D. 50

Answer 1

Answer:

D. 50

Step-by-step explanation:

Let p(x) = x51 + 51 . …(i)

When we divide p(x) by x+1, we get the remainder p(-1)

On putting x= -1 in Eq. (i), we get p(-1) = (-1)51 + 51

= -1 + 51 = 50

Hence, the remainder is 50.

Hope this helps.

Answer 2

Answer:

Let f(x)=x51+51

By remainder theorem, when f(x) is divided by (x + 1), then the remainder = f(−1).

Putting x = −1 in f(x), we get

f(−1)=(−1)51+51=−1+51=50

∴ Remainder = 50

Thus, the remainder when (x51+51) is divided by (x + 1) is 50.

Hence, the correct answer is the option (d).