  We solve the problem of factoring polynomials $V_n(x) \pm 1$ and $W_n(x) \pm
1$ where $V_n(x)$ and $W_n(x)$ are Chebyshev polynomials of the third and
fourth kinds. The method of proof is based on previous work by Wolfram [12] for
factoring variants of Chebyshev polynomials of the first and second kinds,
$T_n(x) \pm 1$ and $U_n(x) \pm 1$. We also show that, in general, there are no
factorizations of variants of Chebyshev polynomials of the fifth and sixth
kinds, $X_n(x) \pm 1$ and $Y_n(x) \pm 1$ using minimal polynomials of
$\cos(\frac{2\pi}{d})$.
