query: Factor $f(x) = x^4+x^2+x+1$ over $F_2$ by using the Berlekamp's algorithm.
positive_passages.docid: 150344
positive_passages.text: Basis of the null space
negative_passages.docid: 129946
negative_passages.text: Synthetic division of polynomials by factor of the form $(ax+b)$
negative_passages.docid: 143107
negative_passages.text: Why is $X^4 + \overline{2}$ irreducible in $\mathbb{F}_{125}[X]$?
negative_passages.docid: 142769
negative_passages.text: Let $f(x) =7x^{32}+5x^{22}+3x^{12}+x^2$. Then find its remainder in the following cases.
negative_passages.docid: 71572
negative_passages.text: factor-square property (FSP) of polynomials
negative_passages.docid: 114529
negative_passages.text: Factoring/Reducing a polynomial $x^4 -2x^3 + 2x^2 + x + 4$
negative_passages.docid: 38871
negative_passages.text: How to obtain the complete factorization of $P_n(X)=\frac{(X+i)^{2n+1} - (X-i)^{2n+1}}{2i} = 0$
negative_passages.docid: 112334
negative_passages.text: Real roots of a polynomial of real co-efficients , with the co-efficients of $x^2 , x$ and the constant term all $1$
negative_passages.docid: 81921
negative_passages.text: If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
negative_passages.docid: 13248
negative_passages.text: How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
negative_passages.docid: 49121
negative_passages.text: Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
negative_passages.docid: 47299
negative_passages.text: Factorize $x^8-x$ over $F_3$ and $F_{81}$
negative_passages.docid: 71482
negative_passages.text: Solve $p_4(x) = x^4 −(2m + 4)x^2 + (m−2)^2 $such that $p_4$ is a product of two non-constant integer-coeficient polynomials
negative_passages.docid: 62615
negative_passages.text: If F is a finite field, then $F^F=P_F$.
negative_passages.docid: 155165
negative_passages.text: Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
negative_passages.docid: 105999
negative_passages.text: An application of derivatives problem- to show that $f(x+2)-f(x)>2$ for $f(x)=x\cos(1/x)$
negative_passages.docid: 113230
negative_passages.text: How can we factor $ q^4 + q^2 + 1$