A supervisor in a logistics center is using the expression $x^2 + bx + c$ to model the distribution of floor space. If both the coefficient $b$ and the constant $c$ are positive, what must be true about the signs of the numbers $m$ and $n$ when factoring the expression into $(x + m)(x + n)$?

A production supervisor uses the trinomial $x^2 + 13x + 40$ to model the efficiency of a new assembly line. Because both the middle term coefficient and the constant term are positive, the supervisor knows that the numbers $m$ and $n$ in the factored form $(x + m)(x + n)$ must both be __________.

A facilities manager is determining the dimensions of a new storage zone with an area represented by the trinomial $x^2 + 11x + 24$. True or False: When factoring this expression into the form $(x + m)(x + n)$, the manager can correctly conclude that both $m$ and $n$ must be positive because the middle coefficient (11) and the constant term (24) are both positive.

A facilities manager is designing a warehouse layout where the floor area is modeled by the expression $x^2 + bx + c$. To determine the dimensions, the manager factors this into the form $(x + m)(x + n)$. Assuming both $b$ and $c$ are positive, match each part of the expression with its correct relationship or requirement.

Determining Factor Signs in Area Models