Question

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.

Answer 1

Answer:

Polynomial expression that represents the area of blanket:

$A(x)=(6x^2+5x-21)cm^2$

If $x=2$: $A(2)=13cm^2$  

Step-by-step explanation:

The area of the rectangle can be calculated with the formula:

$A=lw$

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:

$l=(3x+7)cm$

$w=(2x-3)cm$

Substitute them into  $A=lw$:

 $A(x)=(3x+7)(2x-3)$

Then:

Use Distributive property (Remember the Product of powers property: $b^a*b^c=b^{(a+c)}$ ):

$A(x)=(3x+7)(2x-3)\\A(x)=6x^2-9x+14x-21$

Add like terms:

$A(x)=(6x^2+5x-21)cm^2$ (Simplied form)

Evaluate $x=2$:

$A(2)=(6(2)^2+5(2)-21)cm^2\\A(2)=(6(4)+10-21)cm^2\\A(2)=(24-11)cm^2\\A(2)=13cm^2$