Answer: First option.
Step-by-step explanation:
You need to remember that to factorize the given expression [tex]x^2+10x+21[/tex], you need to choose two numbers that when you add them you get "10" and when you multiply them you get "21".
These number are:
7 and 3
Because:
[tex]7+3=10\\7*3=21[/tex]
Therefore, you get that the factorization of the expression [tex]x^2+10x+21[/tex] is the following:
[tex](x+3)(x+7)[/tex]
You can observe that this factorization matches with the first option.
