\[x^{7} + x^{3} - 4x^{4} - 4 =\]
\[= x^{3}\left( x^{4} + 1 \right) - 4\left( x^{4} + 1 \right) =\]
\[= \left( x^{4} + 1 \right)(x^{3} - 4)\]