Question

find a polynomial that represents the perimeter of the rectangle. perimeter = enter your next step here units

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2l+2w$, where $l$ is the length and $w$ is the width. Here, $l = 4x^{2}+2x + 9$ and $w=x + 5$.

Step2: Substitute values into formula

$P=2(4x^{2}+2x + 9)+2(x + 5)$.

Step3: Distribute the 2s

$P=(2\times4x^{2}+2\times2x+2\times9)+(2\times x+2\times5)=8x^{2}+4x + 18+2x+10$.

Step4: Combine like - terms

$P=8x^{2}+(4x+2x)+(18 + 10)=8x^{2}+6x+28$.

Answer:

$8x^{2}+6x + 28$