Question

1. the perimeter of the polygon is $3x^{3}+2x + 2$. find a polynomial that represents the length of the missing side.

$x + 1$
$2x^{2}+1$

Explanation:

Step1: Find the sum of the known sides

The sum of the known sides is \(x+(x + 1)+(2x^{2}+1)\).
Combine like - terms:

$$
LATEXBLOCK0
$$

Step2: Subtract the sum of known sides from the perimeter

Let the missing side be \(y\). We know that perimeter \(P=x+(x + 1)+(2x^{2}+1)+y\).
Since \(P = 3x^{3}+2x + 2\), then \(y=P-(x+(x + 1)+(2x^{2}+1))\).
Substitute \(P = 3x^{3}+2x + 2\) and \(x+(x + 1)+(2x^{2}+1)=2x^{2}+2x + 2\) into the formula:

$$
LATEXBLOCK1
$$

Answer:

\(3x^{3}-2x^{2}\)