Question

What will be the remainder when the polynomial x power 49 +16 is divided by x+1?

Answer 1

p(x) =x^49+16.
g(x)=x+1 = -1.
then p(-1)=(-1)^49+16=-1+16=15.
hence the remainder will 15

Answer 2

x^49+16 ÷ x+1
___________
x+1 | x^49+16 | x^48
| x^49+x^48 |

Remainder = 16- x^48.

x+1 = 0.
=>x=-1.
Hence,
remainder = 16 - (-1)^48
=16-(1^48) = 16-1
= 15.

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