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:[tex]3x^{2} +2x-7[/tex]                                                                                                                                        Step-by-step explanation:Given : Perimeter of a bigger rectangle is represented by [tex]4x^{2} +5x-2[/tex]Perimeter of a smaller  rectangle is represented by [tex]x^{2} +3x+5[/tex]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 :⇒  [tex]4x^{2} +5x-2 - (x^{2} +3x+5)[/tex]⇒[tex]4x^{2} +5x-2-x^{2} -3x-5[/tex]⇒[tex]3x^{2} +2x-7[/tex]So, Polynomial expression that represents how much larger the first rectangle is than the smaller rectangle is [tex]3x^{2} +2x-7[/tex].