query: method to decompose $x^3+a^3+b^3-3abx=(x+a+b)(x^2+a^2+b^2-ax-bx-ab)$
positive_passages.docid: 19940
positive_passages.text: How to show that $A^3+B^3+C^3 - 3ABC = (A+B+C)(A+B\omega+C\omega^2)(A+B\omega^2+C\omega)$ indirectly?
negative_passages.docid: 108592
negative_passages.text: Given a matrix $A$ with a known Jordan decomposition, what is the Jordan decomposition of $A^2+A+I$?
negative_passages.docid: 136868
negative_passages.text: Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$
negative_passages.docid: 56612
negative_passages.text: Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
negative_passages.docid: 114011
negative_passages.text: Algebra - Solving for three unknowns.
negative_passages.docid: 103763
negative_passages.text: Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$
negative_passages.docid: 134311
negative_passages.text: How to determine equation for $\sum_{k=1}^n k^3$
negative_passages.docid: 103276
negative_passages.text: Solving an equation over the reals: $ x^3 + 1 = 2\sqrt[3]{{2x - 1}}$
negative_passages.docid: 123198
negative_passages.text: Partial Fraction Decomposition?
negative_passages.docid: 55197
negative_passages.text: Roots of $ x^3-3x+1$
negative_passages.docid: 15985
negative_passages.text: simplify $(a_1 + a_2 +a_3+... +a_n)^m$
negative_passages.docid: 64754
negative_passages.text: Find $x$ in the equation $ax^3+bx^2+cx=d$
negative_passages.docid: 70147
negative_passages.text: Solving $x^4 -10x^3 + 26x^2 -10x +1 = 0$.
negative_passages.docid: 3206
negative_passages.text: Given $ax^2+by^2+cxy > 0$, what can I deduce about $a$, $b$, and $c$?
negative_passages.docid: 49744
negative_passages.text: Find remainder of division of $x^3$ by $x^2-x+1$
negative_passages.docid: 65661
negative_passages.text: Decomposition of a homogeneous polynomial
negative_passages.docid: 86841
negative_passages.text: Find a matrix $B$ such that $B^3 = A$