Consider the equation 2cos^2x + sinx - 1 = 0

a) Explain why the equation cannot be factored.

b) Suggest a trigonometric identity that can be used to remove the problem identified in part a).

c) Apply the identity and rearrange the equation into a factorable form.

d) Factor the equation.

e) Determine all solutions in the interval x E [0,2pi].

Ok.. so I tried to factor it. This is my steps:

2cos^2x + sinx - 1 =0

Err i change the way it looks to make it easier for me

2x^2 + x - 1 =0

2x^2 + 2x -1x -1

(2x^2 + 2x) + (-1x - 1)

2x(x+1) -1(x+1)

(2x-1)(x+1)

(2cosx - 1)(cosx + 1)

Isn't that factoring it? Why is it asking why you

**cannot** factor it? What am I doing wrong?