Question

The perimeter of a rectangle is represented by 4x2 + 5x − 2. The perimeter of a smaller rectangle is represented by x2 + 3x + 5. Which polynomial expression BEST represents how much larger the first rectangle is than the smaller rectangle?
A) 3x2 + 2x − 7
B) 3x2 + 2x − 3
C) 3x2 + 8x + 3
D) 5x2 + 8x − 7

Answer 1

$area \: of \: bigger \: rectangle = 4 {x}^{2} + 5x - 2 \\ ara \: of \: smaller \: rectangle = {x}^{2} + 3x + 5 \\ diff = ( 4 {x}^{2} + 5x - 2) - ( {x}^{2} + 3x + 5) \\ = 4 {x}^{2} + 5x - 2 - {x}^{2} - 3x - 5 \\ = 3 {x}^{2} + 2x - 7$
This shows (A) is the right answer.