Find in each case, the remainder when : x 4 + 1 is divisible by x + 1.

x + 1 = 0 ⇒ x = -1. Required remainder = Value of given polynomial x 4 + 1 at x = -1. ∴ Remainder = (-1) 4 + 1 = 1 + 1 = 2. Hence, remainder = 2.

Mathematics

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x + 1 = 0 ⇒ x = -1.

Required remainder = Value of given polynomial x⁴ + 1 at x = -1.

∴ Remainder = (-1)⁴ + 1

= 1 + 1

= 2.

Hence, remainder = 2.

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