I'd like to give my students a little visualization of the fact: $$x^n-a^n=(x-a)(x^{n-1}+x^{n-2}a+\cdots+x a^{n-2}+a^{n-1})$$
So, I've tried:
list = Table[PolynomialQuotient[x^n - a^n, x - a, x], {n, 2, 12}]; Column[list] // TraditionalForm Which gave me the following output.
a+x a^2+a x+x^2 a^3+a^2 x+a x^2+x^3 a^4+a^3 x+a^2 x^2+a x^3+x^4 a^5+a^4 x+a^3 x^2+a^2 x^3+a x^4+x^5 a^6+a^5 x+a^4 x^2+a^3 x^3+a^2 x^4+a x^5+x^6 a^7+a^6 x+a^5 x^2+a^4 x^3+a^3 x^4+a^2 x^5+a x^6+x^7 a^8+a^7 x+a^6 x^2+a^5 x^3+a^4 x^4+a^3 x^5+a^2 x^6+a x^7+x^8 a^9+a^8 x+a^7 x^2+a^6 x^3+a^5 x^4+a^4 x^5+a^3 x^6+a^2 x^7+a x^8+x^9 a^10+a^9 x+a^8 x^2+a^7 x^3+a^6 x^4+a^5 x^5+a^4 x^6+a^3 x^7+a^2 x^8+a x^9+x^10 a^11+a^10 x+a^9 x^2+a^8 x^3+a^7 x^4+a^6 x^5+a^5 x^6+a^4 x^7+a^3 x^8+a^2 x^9+a x^10+x^11 Is there a way I can put the x's before the a's, for example, arranging $$a+x\qquad\text{as}\qquad x+a,$$ and $$a^2+ax+x^2\qquad\text{as}\qquad x^2+xa+a^2,$$ etc.?
