Final answer:
The greatest common monomial factor of the expression 10x^2 + 35x is 5x. When factored out from the expression, it gives us 5x(2x + 7), which corresponds to option D) in the list provided.
Step-by-step explanation:
The greatest common monomial factor of the expression 10x^2 + 35x is the largest monomial that divides both terms. To find it, we look for the greatest common factor of the coefficients and the lowest power of the variable present in both terms. The coefficients 10 and 35 share a greatest common factor of 5, and the lowest power of the variable x that is present in both terms is x (since x^2 has x and 35x has x).
Therefore, the greatest common monomial factor is 5x. If we factor out 5x from the expression, we get 5x(2x + 7). Choosing the correct option from the given ones, D) 5x(2x + 7) would represent the expression factored by the greatest common monomial factor.