Abstract Algebra | Writing a polynomial gcd as a combination -- example. 

QUESTIONS AND CLARITY I agree

If you divide 10 by 11, you can do 10-11= -1 so remainder is -1.

Difference between -1 and 10 is 11. So -1 and 10 are congruent mod 11. Or 10 = -1 (mod11)

the gcd of two polynomials f(x) and g(x) is the monic polynomial of highest possible degree that divides both f(x) and g(x). monic means that there should be no coefficient (i.e. there should only be a coefficient of 1) in front of the leading term, hence he ignores the 11/25. it also makes showing that the remainder is zero easier. he takes care of the 11/25 in the proceeding steps at 11:01 when multiplying 25/11 to g(x). if you included the 11/25 it should work out the same way and cancel out somewhere so that the gcd is monic.

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