Partial fractions with generating functions

[BigBoss22]

Suppose that q(z) = 1, and p(z) = (1 + z)(1 + 3z).

We wish to express q(z)/p(z) in the form

where A and B are constants. To find them, we multiply through by p(z) =
(1 + z)(1 + 3z) and obtain
1 = A(1 + 3z) + B(1 + z)
= (A + B) + (3A + B)z

Im fine up to this point, But according to my notes it is obvious that A + B = 1 and (3A + B)z = 0.

I can not see why this is the case?

Any help would be greatly appreciated.

 

[BigBoss22]

Never mind figured it out:

1 + 0*z = ...

 

[Hurkyl]

Two polynomials are equal iff their coefficients are equal.