Let $f(x)$ be a polynomial such that $f(\cos \theta) = \cos(4\theta)$ for all $\theta$. find $f(x)$. (this is essentially the same as finding $\cos(4\theta)$ in terms of $\cos \theta$; we structure the problem this way so that you can answer as a polynomial. be sure to write your polynomial with the terms in order of decreasing degree.)