Question

The length of a rectangle is given by the function l(x)=12x2+2x+4. The width of the rectangle is given by the function w(x)=3x−1.Which function represents the area of the rectangle?

Answer 1

The area of a rectangle is given by the next equation:

Area = Length * Width

Where

Length =1/2x²+2x+4.

and

Width = 3x−1

Replacing:

Area = (1/2x²+2x+4)* (3x-1)

Solve the operation:

(1/2x²* 3x) + (1/2x²*-1)+(2x*3x)+(2x*-1)+(4*3x)+(4*-1)

Simplify:

3/2x³-1/2x²+6x²-2x+12x-4

= 3/2x³+11/2x²+10x-4

Hence, the correct answer is a(x)=3/2x³+11/2x²+10x-4