query: do $(x+1)^2$ , $(x+2)^2$ , $(x+3)^2$ span all the polynomials to the power of two or less?
positive_passages.docid: 16693
positive_passages.text: Does this set of vectors span the space of all polynomials of degree at most 3?
negative_passages.docid: 134348
negative_passages.text: When is $(p - 1)! + 1$ a power of $p$?
negative_passages.docid: 64878
negative_passages.text: Is this polynomial irreducible in $\mathbb{Q}$?
negative_passages.docid: 13572
negative_passages.text: $x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
negative_passages.docid: 136318
negative_passages.text: Where does the power $2$ come from in the Pythagorean theorem?
negative_passages.docid: 127056
negative_passages.text: How to prove that a polynomial of degree $n$ has at most $n$ roots?
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: 109860
negative_passages.text: Is the number $7$ a polynomial expression.
negative_passages.docid: 109102
negative_passages.text: Determine all real polynomials with $P(0)=0$ and $P(x^2+1)=(P(x))^2+1$
negative_passages.docid: 113168
negative_passages.text: If $a > b$, is $a^2 > b^2$?
negative_passages.docid: 35478
negative_passages.text: Polynomial $p(a) = 1$, why does it have at most 2 integer roots?
negative_passages.docid: 113002
negative_passages.text: Any power of $(X_1, X_2,...,X_i)$ is primary in $k[X_1, X_2,...,X_n].$
negative_passages.docid: 23638
negative_passages.text: $a^2b^2+a^2c^2+b^2c^2\leq 3$
negative_passages.docid: 105395
negative_passages.text: Minimal polynomial of $1 + 2^{1/3} + 4^{1/3}$
negative_passages.docid: 116204
negative_passages.text: Polynomial Remainder Question?
negative_passages.docid: 4310
negative_passages.text: Range of $(a_{1}-a_{2})^2+(a_{2}-a_{3})^2+(a_{3}-a_{4})^2+(a_{4}-a_{1})^2$ is
negative_passages.docid: 117167
negative_passages.text: $3^{n+1}$ divides $2^{3^n}+1$