# I Am Rational (Birthday Quartic)

Algebra Level pending

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 $$rx^2 + sx$$.

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