The area of a rectangular banner is 2,661 square inches. The banner's length x , in

Choice A is correct. It’s given that the banner’s length $x$, in inches, is $24$ inches longer than its width, in inches. It follows that the banner’s width, in inches, can be represented by the expression $x-24$. The area of a rectangle is the product of its length and its width. It's given that the area of the banner is $\mathrm{2,661}$ square inches, so it follows that $\mathrm{2,661}=x\left(x-24\right)$, or $\mathrm{2,661}=x^2-24x$. Subtracting $\mathrm{2,661}$ from each side of this equation yields $0=x^2-24x-\mathrm{2,661}$. Therefore, the equation that represents this situation is $0=x^2-24x-\mathrm{2,661}$.

Choice B is incorrect and may result from representing the width, in inches, of the banner as $24-x$, rather than $x-24$.

Choice C is incorrect and may result from representing the width, in inches, of the banner as $x+24$, rather than $x-24$.

Choice D is incorrect and may result from conceptual or calculation errors.