A manufacturing technician is calculating the dimensions of a rectangular machine part with an area represented by the expression ${}18x^2 - 37xy + 15y^2$. According to the trial and error method, which of the following pairs of binomials correctly represents the dimensions (factors) of this part?

A landscape designer determines that the rectangular area of a custom patio is represented by the trinomial expression ${}18x^2 - 37xy + 15y^2$. Using the trial and error method, they identify that one of the binomial factors representing the dimensions of this patio is $2x - 3y$. The other binomial factor required to represent the area is ____.

A logistics coordinator is calculating the dimensions of a rectangular storage zone where the total area is represented by the expression ${}18x^2 - 37xy + 15y^2$. Place the following steps of the trial and error factoring method in the correct procedural order to find the length and width.

A construction estimator is verifying the dimensions of a rectangular floor plan with an area represented by the algebraic expression ${}18x^2 - 37xy + 15y^2$. True or False: The estimator correctly determines that the binomial factors representing the length and width are $(2x - 3y)$ and $(9x - 5y)$.

A facilities manager is verifying the dimensions of a storage zone on a blueprint where the total area is represented by the expression ${}18x^2 - 37xy + 15y^2$. To factor this expression using the trial and error method, the manager must identify the specific sets of factor pairs for each part of the trinomial. Match each category of algebraic components with its corresponding set of factors.