Math Help - Elementary Algebraic Geometry - Basic Question

1. Elementary Algebraic Geometry - Basic Question

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

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

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

I would appreciate some help with this problem.

Peter

2. Re: Elementary Algebraic Geometry - Basic Question

Sorry everyone - posted the above too quickly

I think solution is

A = a

B = by + d

$C = cy^2 + ey + d$

Peter