A multiplierless discrete cosine transform (DCT) architecture is proposed to improve the power efficiency of image/video coders. Power reduction is achieved by minimizing both the number of arithmetic operations and their bit width. To minimize arithmetic-operation redundancy, our DCT design focuses on Chen's factorization approach and the constant matrix multiplication (CMM) problem. The 8x1 DCT is decomposed using six two-input butterfly networks. Each butterfly is for 2x2 matrix multiplication and requires a maximum of eight adders/subtractors with 13-bit cosine coefficients. Consequently, the proposed 8x1 DCT architecture is composed of 56 adders and subtractors, which represent a reduction of 61.9% and 46.1% in arithmetic operations compared to the conventional NEDA and CORDIC architectures, respectively. To further improve the power efficiency, an adaptive companding scheme is proposed. The proposed DCT architecture was implemented on a Xilinx FPGA. The results from power estimation show that our architecture can reduce the power dissipation by up to 90% compared to conventional multiplierless DCT architectures.