The division algorithm has an analoguen in that asserts: given two polynomials not identically 0, there exists such that

and either

, or

.

Prove this. One route is to proceed by the following steps:

a) If or the degree of is 0, prove the assertion.

b) Proceed by induction on the degree of and assume results for all cases where is of degree less than . Let be of degree .

Subcase (1)

Prove directly

Subcase (2)

Form polynomial and use inductive hypothesis.

OK. If someone could just do the first part of this, a), then I think that MAYBE I can do the rest. Please don't just go and post an entire solution. I really want to try and do some of this. I just can't get started.

Thanks to anyone willing to walk me through this.

Note: The polynomial was discussed in the previous problem here ---> http://www.mathhelpforum.com/math-he...hm-170136.html