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?

Answer 1

4x2 +5x - 2 -x2 +3x +5 Simplified: 3x2 + 8x +3 In order to determine the difference in size, you must subtract the perimeter of the smaller rectangle from the perimeter of the larger rectangle.

Answer 2

Answer:

$3x^{2} +2x-7$                                                                                                                                        

Step-by-step explanation:

Given :

Perimeter of a bigger rectangle is represented by $4x^{2} +5x-2$

Perimeter of a smaller  rectangle is represented by $x^{2} +3x+5$

To Find : Polynomial expression that represents how much larger the first rectangle is than the smaller rectangle.

Solution :

Subtract the equation of perimeter of  smaller rectangle from equation of  perimeter of a bigger rectangle :

⇒  $4x^{2} +5x-2 - (x^{2} +3x+5)$

⇒$4x^{2} +5x-2-x^{2} -3x-5$

⇒$3x^{2} +2x-7$

So, Polynomial expression that represents how much larger the first rectangle is than the smaller rectangle is $3x^{2} +2x-7$.