No, the degree has nothing to do with how many terms.

Remember that the degree of a polynomial is the

**highest power of **.

Since you reduced it down to fractions with quadratic functions (degree 2) in the denominators, that means that the numerators could be anything up to a linear function (degree 1).

And to answer your other question:

You have

.

Notice that I could rewrite the the equation so that it looks like this:

.

The left hand side can only equal the right hand side if the coefficients of like powers of

are equal.

Since the coefficient of

is

, that means for LHS to equal RHS,

.

Similarly, the coefficient of

is

. So for LHS to equal RHS,

.

Using the same logic,

and

.

That gives you four equations in four unknowns that you can solve simultaneously.