Answer
$$2\sin^2 x+3\sin x+1=(\sin x+1)(2\sin x+1)$$
Work Step by Step
$$A=2\sin^2 x+3\sin x+1$$
We would separate $3\sin x$ into $2\sin x$ and $\sin x$.
$$A=(2\sin^2 x+2\sin x)+(\sin x+1)$$
$$A=2\sin x(\sin x+1)+(\sin x+1)$$
$$A=(\sin x+1)(2\sin x+1)$$
