I have a quick question. The problem reads:(adsbygoogle = window.adsbygoogle || []).push({});

Prove that there is no integer m such that 3x^{2}+4x + m is a factor of 6x^{4}+50 in Z[x].

Now, Z[x] is not a field. So, the division algorithm for polynomials does not guarantee us a quotient and remainder. When I tried dividing 6x^{4}+50 by 3x^{2}+4x + m, it immediately would have push me out of the integers. So, 3x^{2}+4x + m cannot be a factor no matter what m is.

My question, how can write that nicely in a proof? This may be a silly question. I have finished my first run through of Pinter's A Book of Abstract Algebra and I am now going back, re-writing proofs more concisely, fixing mistakes, and trying ones I skipped or did not "get." I only wrote an explanation similar to the one above for my answer with an attempt at divinding the polynomials.

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# Homework Help: Computation Question in the Ring of Polynomial with Integer Coefficients

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