A logistics coordinator is using the algebraic expression z^2 - 4z - 5 to model the space requirements for a new warehouse section. Which of the following is the correct factored form of this expression?

A production manager uses the expression z^2 - 4z - 5 to calculate the dimensions of a new workspace. To factor this expression, the manager must find two numbers that multiply to -5 and add to -4. If the manager has already identified 1 as the first number, what is the second number?

A facilities manager is documenting the standard four-step procedure for factoring the expression $z^2 - 4z - 5$ to help new trainees calculate workspace dimensions. Arrange the following steps in the correct order as they appear in the training manual.

A systems analyst is verifying the algebraic logic for a resource allocation formula represented by the expression $z^2 - 4z - 5$. To ensure the formula is correctly factored into $(z + 1)(z - 5)$, match each term or value with its correct role according to the trinomial factoring strategy.

A small business owner is using the algebraic expression $z^2 - 4z - 5$ to model the floor space of a new storage room. When factoring this expression into two binomials, the owner must identify two numbers with opposite signs because the constant term, $-5$, is negative.

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A systems analyst is documenting the differences between two algebraic resource models: $z^2 - 4z - 5$ and $z^2 + 4z - 5$. According to the trinomial factoring strategy, what is the primary difference between the factored forms of these two expressions?

A quality control technician is auditing a technical specification that uses the algebraic model $z^2 - 4z - 5$ for stress testing. To ensure the factored model $(z + 1)(z - 5)$ provided in the documentation is correct, the technician performs a multiplication check. According to the trinomial factoring strategy, which expression represents the correct intermediate step in the expansion of $(z + 1)(z - 5)$ before the middle terms are combined?