Question

Factor the algebraic expression below in terms of a single trig function

Answer 1

This would be
(sin x + 2)(sin x - 1)

Answer 2

You can make it look simpler by doing a substitution.
Let u = sin x.
Then u^2 = sin^2 x.

sin^2 x + sin x - 2 =

Apply the substitution to get

= u^2 + u - 2

Factor

= (u + 2)(u - 1)

Now substitute back sin x for u.

= (sin x + 2)(sin x - 1)