List all the elements of ${\mathbb F_2}[X]/(X^3+X^2+1)$. I just don't get this. Looking through past papers, I came across this problem, Q. Let $F_2$ be a field with 2 elements. Let $P=x^3+x^2+1\in F_2[X]$. $I$ is the ideal of $F_2[X]$ generated by $P$. List all elements of the factor ring $F_2[X]/I$.
My answer; technically, I do get it correct. Having come across similar problems multiple times, I just guessed it'll be in the form $a+bx+cx^2$, where each coefficient is from the said field. Seems like the 2 elements are 0,1 so I can just list all combinations of it.
But, my question is, say what does $1+x^4+I$ become?
I know I should treat $x^3+x^2+1=0$, but substitution doesn't help.
And I cannot "decompose" or maybe factorize $1+x^4$ such that I can get a multiple of $x^3+x^2+1$ and let it be "absorbed' to $I$.
It just confuses me, how I should specifically manipulate $1+x^4$, $1+x^5$, $x^5$ or anything like that. 
Well, if I haven't explained my confusion clearly, simply put;
Would someone please give me steps to obtaining what $1+x^4+I$, $1+x^5+x^7+I$ and so might be, and how I should think about doing it???
Maybe because it's extremely abstract but in the past 3 months, including my lecturer and textbook, no one is really able to explain it with extensive clarity really, or maybe math is just not my thing. 
This idea of Factor Rings, while I can give definitions if asked, just doesn't click.
It would be great if someone can help me out, thanks so much in advance

Use the division algorithm: For $f, g \in F[x]$, there exist $q, r \in F[x]$ such that $f(x) = q(x)g(x)+r(x)$ with $\deg r < \deg g$.
For the example: we wish to interpret $f(x) = x^4+1$ modulo $g(x) = x^3+x^2+1$. Using the division algorithm, we have $$f(x) = (x+1)g(x)+(x^2+x),$$ so $(x^4+1)+I = (x^2+x+(x+1)g(x))+I = (x^2+x)+I$ because $g(x) \in I$.
