An early exercise in the book Algebraic Geometry by Thomas Garrity et. al. is the following:

Exercise 1.1.13. Express the polynomial $\displaystyle P(x,y) = x^2 + bxy + cy^2 + dx + ey + h $ in the form

$\displaystyle P(x,y) = Ax^2 + Bx + C $ where A, B and C are polynomials in y. What are A, B and C?

I would appreciate some help with this problem.

Peter