A construction supervisor is calculating the dimensions of a rectangular foundation where the total area is represented by the polynomial ${}18x^2 - 3xy - 10y^2$. Based on the standard factoring of this specific expression, which of the following represents the correct factored form?

An engineering blueprint represents the cross-sectional area of a support beam using the polynomial expression ${}18x^2 - 3xy - 10y^2$. If a stress analysis confirms that one of the linear factors of this area is $({}3x + 2y)$, the other linear factor must be ____.

A manufacturing technician is calculating the dimensions of a structural plate where the surface area is given by the expression ${}18x^2 - 3xy - 10y^2$. To simplify the design specifications, the technician must factor this expression using the trial and error method. Arrange the following steps in the correct order to complete the factoring process.

A cost estimator is analyzing a production formula simplified from the expression ${}18x^2 - 3xy - 10y^2$. Match each component of the factoring and verification process with its corresponding mathematical result.

A quality control technician is auditing a design specification that represents a structural area with the polynomial ${}18x^2 - 3xy - 10y^2$. The specification states that the completely factored form of this expression is $({}3x + 2y)({}6x - 5y)$. Is the specification's factoring correct?