# Whats the best way to factor this

1. Sep 6, 2014

### shreddinglicks

1. The problem statement, all variables and given/known data

2cos^2(θ) + cos(θ) - 1

2. Relevant equations

2cos^2(θ) + cos(θ) - 1

3. The attempt at a solution

How do I factor this to give me that answer?

2. Sep 6, 2014

### Student100

Do a substitution, x = cos(theta)

Now you have 2x^2 + x -1.

You know the signs of the factors must be a plus and a minus, so ( + ) ( - ) the two on your x squared lets you know that you need a two x. And the 1 tells you both end digits must be 1. (2x-1) (x +1) is the only combination that works to leave you with one quantity of positive x.

3. Sep 7, 2014

### HakimPhilo

Here's an outline of the solution: As pointed out by Student100 the substitution $\cos\theta\leadsto x$ produces a quadratic, and if you know the roots of a quadratic -- say $ax^2+bx+c$ with roots $r_1,r_2$ if any -- then you can factor it as $a(x-r_1)(x-r_2)$. The only step that remains is to “undo” the substitution by replacing $x$ with the original $\cos\theta$. I hope you can achieve all of those steps to find your desired answer. ;-)