Show that if $ax^2+bx+c$ can be factored such that the factors have integer coefficients, then there exists integers $u$ and $v$ such that $u+v=b$ and $uv=ac$.
This problem regards the "diamond method" which was not covered in class. It is used to factor $ax^2+bx+c$. First we find integers $u,v$ such that $u+v=b$ and $uv=ac$. Then we factor $ax^2+ux+vx+c$ by grouping.