A manufacturing design specifies a rectangular part with an area represented by the expression ${}18w^2 - 39w + 18$. To determine the part's dimensions, a technician must factor the expression using the ac method. Arrange the following steps in the correct order to complete this factorization.

A technician is reviewing a design specification that uses the expression ${}18w^2 - 39w + 18$ to model material tension under load. According to the standard procedure for factoring this expression using the $ac$ method, what is the first step the technician should perform, and what is the specific numerical value involved in that step?

A structural engineer is analyzing the load-bearing capacity of a steel beam, modeled by the expression ${}18w^2 - 39w + 18$. To simplify the formula using the $ac$ method, match each component of the factoring process with its correct numerical value or expression.

A technician is optimizing a production formula that involves the expression ${}18w^2 - 39w + 18$. After factoring out the greatest common factor of 3, the expression is rewritten as ${}3(6w^2 - 13w + 6)$. True or False: To continue factoring the inner trinomial using the $ac$ method, the middle term ${}-13w$ is correctly split into ${}-4w$ and ${}-9w$ because their product is 36 and their sum is -13.

A structural detailer is simplifying a load-bearing calculation modeled by the expression ${}18w^2 - 39w + 18$. After factoring out the greatest common factor of 3 to obtain ${}3(6w^2 - 13w + 6)$, the detailer applies the 'ac' method to the inner trinomial. The detailer determines the product $ac$ is 36, and now must recall the procedure to find two numbers that multiply to 36 and add up to the middle coefficient, which is ____.

Quality Control Documentation Review

Manufacturing Quality Control: Factoring Tension Formulas