Question

A rectangular pen, in which chickens and roosters are kept, has a width that is represented with the polynomial w=x3−2x+3x2+15, and a length that is represented with the polynomial l=x4−x2+11x3−5.

Remember that the perimeter of a rectangle can be found using the formula P=2l+2w or P=2(l+w).

Which polynomial represents the perimeter of this pen?

A. x4+12x3+2x2−2x+10
B. 24x3+4x2−4x+15
C. 2x4+24x3+4x2−4x+20
D. 2x4−20x3+4x2−4x+40

Answer 1

The correct option is C.

Explanation:

The width of the rectangular pen is

`w=x^3-2x+3x^2+15`

The length of the rectangular pen is

`l=x^4-x^2+11x^3-5`

The perimeter of a rectangle is

`P=2(l+w)`

`P=2(x^4-x^2+11x^3-5+x^3-2x+3x^2+15)`

`P=2(x^4+12x^3+2x^2-2x+10)`

`P=2x^4+24x^3+4x^2-4x+20`

Therefore the correct option is C.