Question

Candice is an interior designer, and she is currently trying to change the look of a room. Candice found that the area of a room could be given by the expression 3x2 + 2x. The aread of the rug she wants to spread on the floor is given by the expression x2 + 24x - 144. What expression represents the area of the room not covered by the rug?

Answer 1

`A(x) = 2x^2-22x+144`

Explanation:

We are given the following in the question:

Area of room =

`3x^2 + 2x`

Area of rug =

`x^2 + 24x - 144`

We have to find the area of of the room not covered by the rug.

Area of of the room not covered by the rug =

Area of room - Area of rug

`A(x)=(3x^2 + 2x) - ( x^2 + 24x - 144)\\A(x)=3x^2 + 2x-x^2 -24x + 144\\A(x)=(3x^2-x^2)+(2x -24x) + 144\\A(x)=2x^2-22x+144`

is the required expression for the area of floor not covered by the rug.