The Evaluating the Quality of Instruction in Post-secondary Mathematics (EQIPM) is a 14-item instrument that uses videos of teaching to investigate the quality of instruction in college algebra courses taught at community colleges. We hypothesize that quality of instruction can be characterized along three distinct factors, the interactions between: (a) students and the content, (b) instructors and the content, and (c) students and the instructors. We used confirmatory factor analysis to empirically evaluate this hypothesis. Using coding of over 900 segments of video of instruction from 40 intermediate and college algebra teachers from eight community colleges, we performed a factor analysis to identify the structure of the instrument. Our findings suggest that the EQIPM instrument captures the three hypothesized underlying factors of quality of instruction with adequate fit statistics and factor loadings. The availability of this instrument opens the door for further research on aspects of quality that influence student performance and for promising programs of professional development for community college faculty teaching mathematics.