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# Highest common factor watch

1. ind the quotient and remainder when f(X)=X^3+4⋅X^2+3⋅X+15 is divided by g(X)=X^2+3. Hence, find hcf(f(X),g(X)).

I calculated the quorient to be x+4 and the remainder 3/(x^2+3) but not sure how to calculate the hcf.

Thanks!
2. (Original post by Substitution)
ind the quotient and remainder when f(X)=X^3+4⋅X^2+3⋅X+15 is divided by g(X)=X^2+3. Hence, find hcf(f(X),g(X)).

I calculated the quorient to be x+4 and the remainder 3/(x^2+3) but not sure how to calculate the hcf.

Thanks!
Would it not simply be 1?
3. (Original post by Zacken)
Would it not simply be 1?
Maybe, is that because a remainder exists when dividing?
4. (Original post by Substitution)
Maybe, is that because a remainder exists when dividing?
I think it's because is irreducible and the reason you've given.

Edit: I'm going to add in a disclaimer that I don't really know what I'm talking about here - so somebody fele free to jump in and correct me. :-)
5. (Original post by Substitution)
ind the quotient and remainder when f(X)=X^3+4⋅X^2+3⋅X+15 is divided by g(X)=X^2+3. Hence, find hcf(f(X),g(X)).

I calculated the quorient to be x+4 and the remainder 3/(x^2+3) but not sure how to calculate the hcf.

Thanks!
So you have .

Now use the following result let .

If

then

Now from above we have .

In fact for

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