Factor the algebraic expression below in terms of a single trigonometric function. sin 2x + sin x - 2 can somebody show me the steps im so lost

An exponent is customarily indcated using a caret (^), the character above the "6" on most keyboards. People like to write your first term as sin^2(x), but it is perhaps better written as sin(x)^2, the square of sin(x). Note that parentheses are required to identify the argument of the sine function.

You can let some variable stand for sin(x), such as ...
.. z = sin(x)
Now, the expression can be written as
.. z^2 +z -2
This quadratic expression can be factored in the usual way: find two factors of -2 (the constant term) that add to +1 (the coefficient of z).

You know
.. -2 = -1*2 = -2*1
The first factor pair (-1, 2) sums to +1, so we can write the factorization as
.. z^2 +z -2 = (z -1)(z +2)
In terms of the trig function, this is
.. sin(x)^2 +sin(x) -2 = (sin(x) -1)*(sin(x) +2)

The answer is the third choice