Remainder of polynomial division

[songoku]

Is this true?

If the remainder of f(x) / g(x) is a (where a is constant), then the remainder of (f(x))ⁿ / g(x) is aⁿ

I don't know how to be sure whether it is correct or wrong. I just did several examples and it works.

Thanks

 

[fresh_42]

Is this true?

If the remainder of f(x) / g(x) is a (where a is constant), then the remainder of (f(x))ⁿ / g(x) is aⁿ

I don't know how to be sure whether it is correct or wrong. I just did several examples and it works.

Thanks

One way to deal with remainders is to write down what it means, which is always a good point to start at.
Here you have $f(x)=q(x)\cdot g(x) + a$. Now you can work with it.

 

[Delta2]

Hint: Raise both sides of the equation @fresh_42 posts, to the power of n and perhaps use binomial expansion https://en.wikipedia.org/wiki/Binomial_theorem.

 

[songoku]

I tried it and found out it is actually correct.

Thanks a lot for the help