Question

Abstract Algebra: Find the polynomials q(x) and r(x) such that f(x)=g(x)q(x) + r(x), and r(x)=0 OR deg r(x) < deg g(x):
f(x) = 4x^4 + 2x^3 + 6x^2 + 4x + 5 and g(x) = 3x^2 + 2 in Z7[x]

Answer 1

I have absolutely no idea how to even start this.

Answer 2

I would start with long division

Answer 3

do you know how to do long division?

Answer 4

I get \[q(x)=6x^2+3x+5\] and \[r(x)=5x+2\]

Answer 5

Ohhhh okay, so i just do division in Z 7 and. I feel so stupid that I just didn't get that. OKay. Thanks! I'll start doing that now.

Answer 6

yes