Question

How do you write a polynomial in standard form that represents the area of the shaded region of a rectangle when on the outside there are (x+4) and (x+7) and the inside the larger rectangle has (x+2) and (x+5)....the shaded region is in between those two rectangles.

Answer 1

f ( x ) = ( x + 7 ) ( x + 4 ) - ( x + 5 ) ( x + 2 ) =
= ( x² + 4 x + 7 x + 28 ) - ( x² + 2 x + 5 x + 10 ) =
= ( x² + 11 x + 28 ) - ( x² + 7 x + 10 ) =
= x² + 11 x + 28 - x² - 7 x - 10 = 4 x + 18
Answer:
The area of the shaded region is 4 x + 18.