Answer:
B
Step-by-step explanation:
The area of the biggest rectangle =
[tex](9x - 2)(2x + 7) = 18 {x}^{2} + 63x - 4x - 14 = 18 {x}^{2} + 59x - 14[/tex]
The area of the of the smallest rectangle inside=
[tex]3x(x + 12) = 3 {x }^{2} + 36x[/tex]
Then the area of the shaded region =
[tex]18 {x}^{2} + 59x - 14 - (3 {x}^{2} + 36x) = 18 {x}^{2} + 59x - 14 - 3 {x}^{2} - 36x = 15 {x}^{2} + 23x - 14[/tex]
So, we choose B.
