# Tagged Questions

This tag is used for both basic and advanced questions on polynomials in any number of variables. Including, but not limited to: solving for roots, factoring, checking for irreducibility. This tag is rarely used as the only tag for a question.

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### Showing that for $f \in K[x]$, we have $f \mid f(x + f(x))$

Let $K$ be a field an $f \in K[x]$. I now want to show that $f(x) \mid f(x + f(x))$ (in $K[x]$). I know that I need to find a polynomial $g \in K[x]$ so that $f(x) g(x) = f(x + f(x))$. So I thought ...
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### (Terminology_Taylor Series) “expand at $x_0$, evaluate at x, affine approximation”

I am reading one-variable calculus book where it explains Taylor series and little confused with the following terms: (1) Expand $f(x)$ at $x_0$ (2) Evaluate $f(x)$ at x (3) Best Affine, ...
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### In an $\Bbb{N}$-graded domain $A$, units are homogeneous

Let $A$ be a graded domain, with additive subgroups $A_n,\,\forall\,n\geq 0$, s.t. ${A_n\cdot A_m}\subseteq A_{n+m}\,\forall\,n,m\geq 0$, and $A=\bigoplus_{n=0}^\infty\, A_n$ as abelian groups. I wish ...
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### Fast way of suming up polynoms

You probably will think that this question is more about algorithms, but actually i'am searching for right formula. What i want to do is to compute $(A^n + A^{n-1} + .. + A + 1))$ mod $(10^9 + 7)$ ...
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### Radius of Convergence for Polynomial

I have to find the radius of convergence for this one, but I haven’t found a solution for this type of a term. $\mathbb f (x)$ = $1 + 7x^3 + 5x^4 + x^{13} + x^{2015}$ Could you help me out?