Question

Write a polynomial that describes the area of the shaded region.

The area of the shaded region is cubic units.
(Simplify your answer. Type an expression using x as the variable.)
N
N
X+7

Answer 1

so if we take the area of the whole square that's shaded, and then subtract from it the area of the square that's not shaded, what's leftover is the area we never subtracted, namely the shaded region.

`\stackrel{ \textit{shaded square} }{(x+7)(x+7)}~~ - ~~\stackrel{ squarish~hole }{(2)(2)}\implies \stackrel{\textit{F O I L}}{(x^2+14x+49)-4} \\\\\\ ~\hfill~ x^2+14x+45~\hfill~`

Answer 2

The polynomial that describes the area of the shaded region is x^2 + 7 (cubic units).

Step-by-step explanation:

The polynomial that describes the area of the shaded region is x^2 + 7 (cubic units). Since the area of the shaded region is given in cubic units, the polynomial must have a degree of 3. The expression x^2 + 7 is a cubic polynomial with a leading term of x^2, indicating a degree of 2, and a constant term of 7, which represents the shaded region.