Question

expression of ax^2 + bxy +cy^2 ​

Answer 1

Answer:

What you have is a homogeneous polynomial of degree 2 in x and y (homogeneous means that the total degree is the same in each monomial).

Divide through by y2, and set Z=xy. (This is called "de-homogeneization"). This will give you the one-variable degree 2 polynomials

aZ2+bZ+c.

If you know how to factor these (which is not hard), then after factoring

aZ2+bZ+c=(rZ+s)(tZ+u)

you can multiply through by y2 by multiplying one y in each factor on the right hand side, to get back to the homogeneous form ("homogeneization"):

ax2+bxy+cy2=(rx+sy)(tx+uy).

So it all comes down to factoring degree 2 polynomials.

Step-by-step explanation: