I have the following polynomial that I want to factor $$ \begin{align*} p(x)= &- 236364091 x^{13}- 28363690920 x^{12}- 1487737229594 x^{11}\\ &- 44880832661940 x^{10} - 860924276925225 x^9- 10941278514219396 x^8 \\ &- 92883153994532540 x^7 - 516122234647942344 x^6 - 1766587850009264989 x^5 \\ &- 3172232270188300464 x^4 - 1263789594225408906 x^3 + 3700632893619477564 x^2 \\ &+ 3120329011246701345 x+5179915266025500 \\ \end{align*} $$ I suspect that $(x+24)$ and $(x+25)$ are factors. I'm interested in the remaining polynomial $q(x)$ such that $p(x)=(x+24)(x+25)q(x)$. I've tryed Mathematica with no success. Can anyone help?
I'm also interested in other software packages more suited to the factorization of this kind of polynomials.
Thanks.
I'm back!!!
Unfortunately there was an error in the above polynomial, so it didnt factor as expected. The correct one follows $$ \begin{align*} p(x)= &-2363640910 x^{13}- 283636909200 x^{12}- 14830715886140 x^{11} \\ &-445215783064800 x^{10}- 8492530754498370 x^9- 107310315789497520 x^8 \\ &- 905953817318009480 x^7- 5008244551318927680 x^6- 17061651312407299570 x^5\\ &- 30494240185050800880 x^4- 12007914756669549180 x^3 + 35636084573032450080 x^2\\ &+ 29908147265568403650 x +103598305320510000 \end{align*} $$ and factors as expected to: $$ \begin{align*} p(x)=-10 (24 + x) (25 + x) q(x) \end{align*} $$ where $$ \begin{align*} q(x)=&236364091 x^{11}+ 16781850461 x^{10}+518942461425 x^9\\ &+ 9024287420055 x^8 + 95697515012142 x^7+ 627280891321794 x^6\\ &+ 2440109049747842 x^5+ 4890576901172110 x^4+ 2461433234591367 x^3\\ &- 5532350693162895 x^2- 4983281122883427 x-17266384220085 \end{align*} $$ Thanks, next time I'll think twice...
This function has no factorization in $\mathbb{Q}$. I did a manual check with Mathematica.