What will be remainder when we divide (x71 + 71) by (x + 1) ?

Step-by-Step Solution

To find the remainder when a polynomial P(x) is divided by (x - a), you can use the Remainder Theorem, which states that the remainder is equal to P(a).

1. Define the polynomial and divisor:

   • P(x) = x^71 + 71

   • Divisor = x + 1

2. Apply the Remainder Theorem:

   • Set the divisor to zero to find the value to substitute: x + 1 = 0, so x = -1.

   • The remainder is P(-1).

3. Calculate P(-1):

   • P(-1) = (-1)^71 + 71

   • Since 71 is an odd number, (-1) raised to the power of 71 is -1.

   • P(-1) = -1 + 71

   • P(-1) = 70.

The remainder when (x^71 + 71) is divided by (x + 1) is 70.