In this paper, we propose a rank-one tensor modeling approach that yields a compact representation of the optimum IRS phase-shift vector for reducing the feedback overhead. The main idea consists of factorizing the IRS phase-shift vector as a Kronecker product of smaller vectors, namely factors. The proposed phase-shift model allows the network to trade-off between achievable data rate and feedback reduction by controling the factorization parameters. Our simulations show that the proposed phase-shift factorization drastically reduces the feedback overhead, while improving the data rate in some scenarios, compared to the state-of-the-art schemes.