As an estimator for a construction firm, you use the expression ${}20x^2 - 16x - 15x + 12$ to model material ordering needs. When applying the grouping method to factor this expression, you first extract ${}4x$ from the first two terms to get ${}4x(5x - 4)$. Based on the steps of the grouping method, what value must be factored out of the remaining terms, $-15x + 12$, to reverse the signs and reveal the exact same common binomial factor of ${}5x - 4$?

An inventory specialist is calculating the dimensions of a warehouse storage zone. The total area is modeled by the polynomial ${}20x^2 - 16x - 15x + 12$. To find the individual dimensions (length and width), the specialist must factor the expression using the grouping method. Arrange the following steps in the correct order to complete the factoring process.

A production analyst is simplifying a cost-efficiency model represented by the polynomial ${}20x^2 - 16x - 15x + 12$. To present a clearer formula to the management team, the analyst must factor the expression using the grouping method. Match each mathematical component of this process with its specific role.

A budget analyst is simplifying a cost-projection formula represented by the polynomial ${}20x^2 - 16x - 15x + 12$. By applying the grouping method, the analyst has reached the intermediate step: ${}4x(5x - 4) - 3(5x - 4)$. What is the common binomial factor that must be factored out next to reach the final simplified form?

A financial analyst is simplifying a projected revenue model represented by ${}20x^2 - 16x - 15x + 12$. When applying the grouping method, the analyst factors out ${}4x$ from the first two terms to get ${}4x(5x - 4)$. To complete the grouping process correctly, the analyst must factor out a positive 3 from the remaining terms, $-15x + 12$, to produce a matching binomial of ${}5x - 4$.

Polynomial Modeling for Space Optimization

Warehouse Floor Plan Optimization