# Thread: Simple polynomial division question

1. ## Simple polynomial division question

Hello

I hope someone can help me with this.

Let's say I want to divide x^2 + x + 1 into x^2 + 1

Am I right in thinking the answer is 1 remainder x?

This is how I am getting my answer...

I convert my polynomials into binary -

x^2 + x + 1 = 111
x^2 + 1 = 101

Then I do long division -

Code:
        1
111 / 101
111
----
010
Which translates as 1 remainder x.

Am I correct?

If so, how would I handle x^4 + 1 into x^2 + 1?

Convert to binary -

10001 / 101

Am I right in thinking the answer is -

Code:
          0
10001 / 101
000
----
101
So the answer is 0 remainder x^2 + 1?

Thank you.

2. Originally Posted by MrSteve
Hello

I hope someone can help me with this.

Let's say I want to divide x^2 + x + 1 into x^2 + 1

Am I right in thinking the answer is 1 remainder x?

This is how I am getting my answer...

I convert my polynomials into binary -

x^2 + x + 1 = 111
x^2 + 1 = 101

Then I do long division -

Code:
        1
111 / 101
111
----
010
Which translates as 1 remainder x.

Am I correct?

If so, how would I handle x^4 + 1 into x^2 + 1?

Convert to binary -

10001 / 101

Am I right in thinking the answer is -

Code:
          0
10001 / 101
000
----
101
So the answer is 0 remainder x^2 + 1?

Thank you.

Your method will work, I think, when the coefficients of both polynomials are either zero or one.

3. Hi,

the first part what u did it is correct.

for the second part that is when x^4+1 divided by x^2+1
the remainder will be -x^2+1 and quotient is x^2.

4. Originally Posted by tutor
for the second part that is when x^4+1 divided by x^2+1
the remainder will be -x^2+1 and quotient is x^2.
Hello

I am not too worried about it being -x^2 + 1 or x^2 + 1 (in my code, whether I XOR a minus or a plus, the answer is the same), but I do not understand why the coefficient is x^2.

I am dividing x^2 + 1 by x^4 + 1. Do you think I am doing it the other way round?

Thanks

5. Originally Posted by tutor
Hi,

the first part what u did it is correct.

for the second part that is when x^4+1 divided by x^2+1
the remainder will be -x^2+1 and quotient is x^2.
The original question says into, not by .....