To factor the quadratic expression \( g^2 + 13g + 30 \), we need to find two numbers that multiply to \( 30 \) (the constant term) and add up to \( 13 \) (the coefficient of the \( g \) term).
The pairs of factors of \( 30 \) are:
- \( 1 \) and \( 30 \)
- \( 2 \) and \( 15 \)
- \( 3 \) and \( 10 \)
- \( 5 \) and \( 6 \)
Among these pairs, the pair that adds up to \( 13 \) is \( 3 \) and \( 10 \).
Now we can write the quadratic in its factored form:
\[ g^2 + 13g + 30 = (g + 3)(g + 10) \]
So the factored form of \( g^2 + 13g + 30 \) is:
\[ (g + 3)(g + 10) \]