Difference between revisions of "Common factorizations"
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*<math>x^3-y^3=(x-y)(x^2+xy+y^2)</math> | *<math>x^3-y^3=(x-y)(x^2+xy+y^2)</math> | ||
| − | *<math>x^{2n+1}+y^{2n+1}=(x+y)(x^{2n}-x^{2n-1}y+x^{2n-2}y^2-\ldots-xy^{2n-1}+y^{2n})</math> | + | *<math>x^{2n+1}+y^{2n+1}=(x+y)(x^{2n}-x^{2n-1}y+x^{2n-2}y^2-\ldots-xy^{2n-1}+y^{2n})</math> |
| − | *<math>x^{n}-y^{n}=(x-y)(x^{n-1}+x^{n-2}y+\cdots +xy^{n-1}+y^n)</math> | + | *<math>x^{n}-y^{n}=(x-y)(x^{n-1}+x^{n-2}y+\cdots +xy^{n-1}+y^n)</math> |
== Vieta's/Newton Factorizations == | == Vieta's/Newton Factorizations == | ||
Revision as of 03:12, 6 July 2023
These are common factorizations.
Contents
Basic Factorizations
Vieta's/Newton Factorizations
These factorizations are useful for problem that could otherwise be solved by Newton sums or problems that give a polynomial, and ask a question about the roots. Combined with Vieta's formulas, these are excellent, useful factorizations.
