A polynomial commitment scheme is a protocol where a prover commits to a certain polynomial and produces a proof that the commitment is valid. When creating a commitment for verifiable secret sharing, make sure to verify the degree of the committed polynomial (i.e., the number of coefficients sent by the generating party). More technically, given two witnesses to a constraint system, the verifier can combine their commitments into a witness commitment for something called a relaxed R1CS, which is an R1CS instance along with a scalar u and an error vector e. The error vector is used to “absorb” the cross terms generated by combining the two commitments, and the scalar is used to “absorb” multiplicative factors.