How to solve abstract algebra questions

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Question description

I have a doubt in this proof:

20140327194335selection_002.png




My doubt was reduced to the last paragraph, I understood that there are some g_1,g_2 such that f_1g_1 f_2g_2 has leading coefficient 1 and degree ≤d−1 but why by row operations we can suppose for some i≠1,2, f_i=f_1g_1 f_2g_2?

Thanks


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(Top Tutor) Daniel C.
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