# Finding value of $m$ such that such that the polynomial is factorized

A polynomial $2x^2+mxy+3y^2-5y-2$ Find the value of $m$ much that $p(xy)$ can be factorized into two linear factors

• Shouldn't it be $p(x,y)$, not just $p(x)$? – Gregory Grant May 24 '15 at 15:31

Putting $m = 7$ you obtain \begin{align*} (x+3y+1)(y+2x-2) &= xy+2x^2-2x+3y^2+6xy-6y+y+2x-2 \\ &= 2x^2 + 7xy +3y^2-5y-2 \end{align*}
Solve $p(x,y) = 0$ for $x$. Roots are $q_1(y)$ and $q_2(y)$. You will obtain a representation $p = (x - q_1)(x - q_2)$. Now find $m$ that makes $q$ into linear expressions.