What is the remainder when #x^15+5x^8-1# is divided by #x+1#?

1 Answer
Shwetank Mauria
May 31, 2017

The remainder is #3#

Explanation:

Here we are dividing a polynomial of degree #15# by a binomial of degree #1#. Dividing using long division or synthetic division in such cases will be a very long drawn process.

The alternative to this is to use remainder theorem, which is used to identify remainder when a polynomial #P(x)# is divided by a binomial of degree #1#, say #(x-a)#. The remainder is then #P(a)#.

Hence when #x^15+5x^8-1# is divided by #(x+1)# or #(x-(-1))#, the remainder is

#P(-1)=(-1)^15+5(-1)^8-1=-1+5-1=3#

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