I Am Rational (Birthday Quartic)

Let your birthday be expressed as mm/dd/yy where the integer $M$ is the digits mm, $D$ is the digits dd, and $Y$ is the digits yy. Now let $f(x) = Mx^4 + bx^3 + Dx^2 +Y$ . Find $b$ such that $f(x)$ has a rational factor $g(x)$ where $f(x)/g(x)$ has middle terms $(D+Y)x^2 -Yx$ . For example, the middle terms of the factor $(qx^3 + rx^2 + sx +t)$ are $rx^2 + sx$ .