How to Reduce a System of Polynomials

I'm wondering if it is possible to reduce a system of polynomial equations with symbolic coefficients in MatLab. Basically I need to go from:

a00*x_1^2 + a01*x_2^2 + a02*x_3^2 + a03*x_1*x_2 + a04*x_1*x_3 + a05*x_2*x_3 = b0
a10*x_1^2 + a11*x_2^2 + a12*x_3^2 + a13*x_1*x_2 + a14*x_1*x_3 + a15*x_2*x_3 = b0
a20*x_1^2 + a21*x_2^2 + a22*x_3^2 + a23*x_1*x_2 + a24*x_1*x_3 + a25*x_2*x_3 = b0

to three polynomials where 1 has only x_3 (for example), 1 has x_3 and x_2 and the last has x_3, x_2 and x_1.

I have tried using solve but it tries to find an exact solution. It can't find one because the polynomial degrees get too large to solve (at least I imagine that's why it doesn't work), so I need something else. Is this possible to do?

[Walter Roberson]

It isn't that the degree gets too high. If you solve step by step, then after just two steps, you are dealing with a quartic with not-short coefficients, and you know how long the explicit solution of even a simple quartic gets!