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

Answer:

The correct option is C.

Step-by-step 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.