Factor. \[ g^{2}+5 g+6 \]

To factor the expression \( g^{2}+5g+6 \), we look for two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of the \( g \) term). The numbers 2 and 3 fit this criteria perfectly! Thus, we can write: \[ g^{2}+5g+6 = (g+2)(g+3) \] Now, if you want to check your work, you can simply expand the factored form back out to ensure it equals the original expression, which is always a fun way to confirm your factorization skills! Next time, when dealing with quadratic expressions, remember to start by identifying the coefficient relationships; it's like a little puzzle waiting to be solved!