query: Polynomial division over an extension
positive_passages.docid: 14270
positive_passages.text: Polynomial divisibility is unchanged by coeff. field extension
negative_passages.docid: 127524
negative_passages.text: how to find the remainder when a polynomial $p(x)$ is divided my another polynomial $q(x)$
negative_passages.docid: 45117
negative_passages.text: How does polynomial long division work?
negative_passages.docid: 20613
negative_passages.text: Units (invertibles) of polynomial rings over a field
negative_passages.docid: 146591
negative_passages.text: Inseparable polynomial over a non-perfect field
negative_passages.docid: 48873
negative_passages.text: Let $K$ be a field and $f(x)\in K[X]$ be a polynomial of degree $n$. And let $F$ be its splitting field. Show that $[F:K]$ divides $n!$.
negative_passages.docid: 65661
negative_passages.text: Decomposition of a homogeneous polynomial
negative_passages.docid: 55509
negative_passages.text: Factor a polynomial over the reals
negative_passages.docid: 14836
negative_passages.text: A polynomial sequence
negative_passages.docid: 132317
negative_passages.text: linear algebra over a division ring vs. over a field
negative_passages.docid: 85525
negative_passages.text: Prove that $x^3+x+1$ splits in $Z_2[x]/(x^3+x+1)$
negative_passages.docid: 21578
negative_passages.text: Showing the minimal polynomial for an element in an extension field is the same as the minimal polynomial of a linear transformation.
negative_passages.docid: 118411
negative_passages.text: Computing the coefficient in a large polynomial
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: 116204
negative_passages.text: Polynomial Remainder Question?
negative_passages.docid: 40502
negative_passages.text: The Degree of Zero Polynomial.
negative_passages.docid: 134699
negative_passages.text: Can *any* real polynomial be factored linearly (plus a constant) over $\mathbb{R}$?