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How do I factor this polynomial: $2x^2-5xy-y^2$ ?

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    Do you know how to factor $2x^2 - 5x - 1$?2012-05-25
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    It doesn't have an iteger factorization. The only candidates are (2x+y)(x-y) and (2x-y)(x+y) but the first expands to 2x^2-xy-y^2 and the second to 2x^2+xy-y^2.2012-05-25
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    @TonyK i tried, but it didnt work.. :(2012-05-25
  • 2
    Are you sure there is no typo? Perhaps one of the following was intended. $$ 2x^2 -xy-y^2\ =\ (x-y)(2x+y)$$ $$ 2x^2 -5xy-3y^2\ =\ (x-3y)(2x+y)$$ $$ 2x^2 -5xy+2y^2\ =\ (x-2y)(2x-y)$$ $$ 2x^2 -5xy+3y^2\ =\ (x-y)(2x-3y)$$2012-05-25
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    Two possible factorizations are $$\begin{eqnarray*} 2x^{2}-5xy-y^{2} &=&2\left( x-\frac{5+\sqrt{33}}{4}y\right) \left( x-\frac{5- \sqrt{33}}{4}y\right) \\ &=&-\left( y+\frac{5-\sqrt{33}}{2}x\right) \left( y+\frac{5+\sqrt{33}}{2} x\right) \end{eqnarray*}$$2012-08-31

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