When factoring a trinomial of the form $x^2 + bx + c$ where the constant term $c$ is positive and the middle coefficient $b$ is also positive, the two numbers $m$ and $n$ in the factored form $(x + m)(x + n)$ must both be positive. This follows from the sign rules for arithmetic. In the expansion $(x + m)(x + n) = x^2 + (m + n)x + mn$, the last term $c = mn$ is the product of $m$ and $n$. A positive product requires the factors to have the same sign (both positive or both negative). The middle coefficient $b = m + n$ is the sum of $m$ and $n$. Since a positive sum of numbers with the same sign can only occur if both are positive, both $m$ and $n$ must be positive. Therefore, when searching for factor pairs of $c$, only positive pairs need to be tested. The factored expression will be written using addition in both binomials: $(x + m)(x + n)$.