A logistics coordinator is analyzing the total volume of two cube-shaped storage containers, represented by the expression $x^3 + 27$. To simplify their capacity report, they must write this expression in its completely factored form using the sum of cubes pattern. Which of the following is the correct factored form of $x^3 + 27$?

A warehouse planner is calculating the dimensions of a storage unit whose total volume is modeled by the algebraic expression $x^3 + 27$. In the system documentation, they record the completely factored form of this volume model as $(x + 3)(x^2 + 3x + 9)$.

A design engineer is analyzing the volume of a cubic storage unit, modeled by the expression $x^3 + 27$. To simplify the design software's calculations, the engineer must apply the sum of cubes factoring pattern: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. Match each algebraic component of this factoring pattern to its correct value for the expression $x^3 + 27$.

An inventory clerk is updating the volume formulas for cubic storage bins in a company database. One model has a total volume represented by the expression $x^3 + 27$. Arrange the following steps in the correct order to factor this expression using the sum of cubes pattern.

Project Documentation: Volume Factoring

Script Optimization for Container Volumes

A logistics supervisor is calculating the combined volume of two cubic storage container models used in a warehouse, which is represented by the algebraic expression $x^3 + 27$. To simplify their inventory database formulas, they factor this expression using the sum of cubes pattern, yielding $(x + 3)(x^2 - 3x + k)$. The value of the constant integer $k$ in the trinomial factor is ____.