Question

The volume of a box is given by the expression

x + 3x - x-3. The height of the box is given by the expression x-1.
Find an expression for the area of the base of the box.
A.
x2 + 4x + 3
B.
x2 + 2x-3
9
C.
x²+2x
D.
x + 3

Answer 1

Area = x^2+4x+3

Explanation:

The volume of a box is given by the expression

x^3 + 3x^2 - x-3. The height of the box is given by the expression x-1.

volume of the box = Length * width * height

L is the side length of the box;

Given

V(x) = x^3 + 3x^2 - x-3

Factorize

V(x) = x^2(x+3)-1(x+3)

V(x) = (x^2-1)(x+3)

V(x) = (x+1)(x-1)(x+3)

V = LWH

V = Area * Width

Since the height of the box is x - 1

Area = (x+1)(x+3)

Expand

Area = x^2+3x+x+3

Area = x^2+4x+3