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To factorize 5m + 10, you must first look at both terms and find common relations between them. For example, we see that only one term has an m, but both terms are divisible by 5. In this case, 5 is our greatest common factor. To complete this factorization, we would place 5 outside the parentheses, and m and 2 in the parentheses: 5(m+2). By putting 5 outside, we would distribute, or multiply, 5 to the first term, or m, making it 5m, and then multiply 5 to two so we get the second part which is equal to ten. 
[tex]5m+10 \\ \\ GCF = 5 \\ \\ 5( \frac{5m}{5} + \frac{10}{5}) \ / \ factor \ out \ GCF \\ \\ 5(m+2) \ / \ simplify terms \\ \\ Answer: \fbox {5(m + 2)} [/tex]
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