Write a polynomial that represents the perimeter of the figure.

The standard form of a polynomial means, writing the polynomial in descending powers of the variable.

In algebra, like terms are the terms that have the same variables and powers.

The unlike terms are two or more terms that are not like terms.

Perimeter of a figure is the sum of the lengths of all the sides of the figure.

Simplify the given difference by combining the like terms.

Add the lengths of all sides of the given figure.

The perimeter is

$\begin{array}{l}\left(5x^2\right)+\left(4x\right)+\left(4x\right)+\left(3x^3\right)+\left(x^2\right)+\left(1\right)+\left(x\right)+\left(1\right)+\left(6x\right)+\left(8x^4\right)\\ =5x^2+4x+4x+3x^3+x^2+1+x+1+6x+8x^4\end{array}$

Simplify by combining the like terms

$$\begin{gathered} 5x^2+4x+4x+3x^3+x^2+1+x+1+6x+8x^4 \\ =8x^4+5x^2+x^2+4x+4x+x+6x+1+1 \\ =8x^4+6x^2+15x+2 \end{gathered}$$

So the perimeter$=8x^4+6x^2+15x+2$

Therefore the polynomial$8x^4+6x^2+15x+2$represents the perimeter of the given figure.