#### Answer

$$\cot^4x+3\cot^2x+2=(\cot^2x+1)(\cot^2x+2)$$

#### Work Step by Step

$$A=\cot^4x+3\cot^2x+2$$
We would rewrite $3\cot^2 x$ into $(\cot^2 x+2\cot^2 x)$.
$$A=\cot^4 x+\cot^2x+2\cot^2x+2$$
$$A=\cot^2x(\cot^2x+1)+2(\cot^2x+1)$$
$$A=(\cot^2x+1)(\cot^2x+2)$$