Zero-Knowledge in PLONK paper in prover round 3. Shouldn't the degree be less than n?

Question

From the PLONK paper.

On page 29, in the prover algorithm round 3, we divide the quotient polynomial into three polynomials of degree < n. But when we add the blinding terms we add $X^n$.

The question is, how do we commit to this, if we only have n variables in the trusted setup?

Answer 1

Check the "Common preprocessed input:" in the Plonk Paper, page 27.

The SRS for a setup with $n$ gates has all the elements required to commit a polynomial of upto degree $n + 5$, so there is no problem to commit a polynomial of degree $n$.