A warehouse supervisor is comparing two inventory reports to calculate the net difference in items between two zones. The calculation requires finding the difference of two polynomials: $(8x^2 + 3x - 19) - (7x^2 - 14)$. Match each stage of the subtraction process to the correct algebraic representation.

A retail data analyst is calculating the variance between two seasonal sales projections represented by the polynomials $(8x^2 + 3x - 19)$ and $(7x^2 - 14)$. To find the net difference using the expression $(8x^2 + 3x - 19) - (7x^2 - 14)$, arrange the following simplification steps in the correct standard order.

A facility manager is comparing the monthly utility costs of two different buildings. Building A's costs are modeled by the polynomial ${}8x^2 + 3x - 19$, and Building B's costs are modeled by ${}7x^2 - 14$. To find the difference in cost between Building A and Building B, the manager simplifies the expression $(8x^2 + 3x - 19) - (7x^2 - 14)$. Which of the following is the resulting simplified polynomial?

To find the difference of two polynomials, such as $(8x^2 + 3x - 19) - (7x^2 - 14)$, you must change the sign of every term in the second polynomial before combining like terms.

Distributing Subtraction in Performance Metrics

A logistics coordinator is calculating the discrepancy between projected shipments, $(8x^2 + 3x - 19)$, and actual shipments, $(7x^2 - 14)$. When setting up the calculation $(8x^2 + 3x - 19) - (7x^2 - 14)$, the coordinator must first distribute the subtraction operation. This is done by multiplying each term in the second polynomial by ____ to change their signs.