Final answer:
The expression 11 - 10m^2 - 53m cannot be factored by grouping, as it does not conform to the structure usually required for this method and no integers satisfy the required conditions for factoring.
Step-by-step explanation:
The student's question asks to factor by grouping the expression 11 - 10m2 - 53m. Unfortunately, the given expression does not readily lend itself to the common factor by grouping approach, as it would involve three terms, where typically four terms are better suited for this method. However, one can still try to factor a quadratic equation by looking for two numbers that multiply to the product of the coefficient of the quadratic term (-10) and the constant term (11), and also add to the coefficient of the linear term (-53). In this case, such numbers do not exist, which suggests that the expression cannot be factored over the integers. It may be possible to factor over the real numbers, but that usually requires the quadratic formula and is not typically referred to as 'factoring by grouping.'