Write a polynomial expression, in simplified form, that represents the AREA of the blanket and use the expression to evaluate the AREA of the blanket if x = 2.
Accepted Solution
A:
Answer: Polynomial expression that represents the area of blanket: [tex]A(x)=(6x^2+5x-21)cm^2[/tex] If [tex]x=2[/tex]: [tex]A(2)=13cm^2[/tex] Step-by-step explanation: The area of the rectangle can be calculated with the formula: [tex]A=lw[/tex] Being l the lenght of the rectangle and w the width of the rectangle. In this case, the lenght and the width are represented with: [tex]l=(3x+7)cm[/tex] [tex]w=(2x-3)cm[/tex] Substitute them into [tex]A=lw[/tex]: [tex]A(x)=(3x+7)(2x-3)[/tex] Then: Use Distributive property (Remember the Product of powers property: [tex]b^a*b^c=b^{(a+c)}[/tex] ): [tex]A(x)=(3x+7)(2x-3)\\A(x)=6x^2-9x+14x-21[/tex] Add like terms: [tex]A(x)=(6x^2+5x-21)cm^2[/tex] (Simplied form) Evaluate [tex]x=2[/tex]: [tex]A(2)=(6(2)^2+5(2)-21)cm^2\\A(2)=(6(4)+10-21)cm^2\\A(2)=(24-11)cm^2\\A(2)=13cm^2[/tex]