Math Is Fun Forum

Arman Ansary

Member

Registered: 2017-10-07

Posts: 4

Remainder Theorem

This was in my book:
The remainder when x^45 is divided by x^2 - 1 is :-
a)2x
b)-x
c)0
d)x
e)None of these

THIS WAS UNDER THE LEVEL 1 QUESTION SECTION.
Try to answer and it would be good if you show the method.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Remainder Theorem

hi Arman Ansary

Welcome to the forum.

Start by writing

where Q is the quotient and R the remainder, both functions of x.

R must be a linear function (ax + b) because if it had higher power of x, you would be able to further divide it by x^2 -1

If you put x=1 you will get one equation with a and b; and putting x = -1 will give another.  Together you can solve for a and b.

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: Remainder Theorem

Its easy.

Don't you think it should be in Help Me.

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Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Remainder Theorem

Yes but I'm just being helpful anyway.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob