What is factor (x^{624}-1)/(x-1) ?

The solution to factor (x^{624}-1)/(x-1) is

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factor (x^{624}-1)/(x-1)

factor

\frac{x ^{624} - 1}{x - 1}

(x^{8} + 1) (x^{96} - x^{88} + x^{80} - x^{72} + x^{64} - x^{56} + x^{48} - x^{40} + x^{32} - x^{24} + x^{16} - x^{8} + 1) (x^{4} + 1) (x^{48} - x^{44} + x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1) (x^{2} + 1) (x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1) (x + 1) (x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1) (x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1) (x^{416} + x^{208} + 1)

Solution steps

\frac{x ^{624} - 1}{x - 1}

Factor

x^{624} - 1 : (x^{8} + 1) (x^{96} - x^{88} + x^{80} - x^{72} + x^{64} - x^{56} + x^{48} - x^{40} + x^{32} - x^{24} + x^{16} - x^{8} + 1) (x^{4} + 1) (x^{48} - x^{44} + x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1) (x^{2} + 1) (x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1) (x + 1) (x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1) (x - 1) (x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1) (x^{416} + x^{208} + 1)

= \frac{( x ^{8} + 1 ) ( x ^{96} - x ^{88} + x ^{80} - x ^{72} + x ^{64} - x ^{56} + x ^{48} - x ^{40} + x ^{32} - x ^{24} + x ^{16} - x ^{8} + 1 ) ( x ^{4} + 1 ) ( x ^{48} - x ^{44} + x ^{40} - x ^{36} + x ^{32} - x ^{28} + x ^{24} - x ^{20} + x ^{16} - x ^{12} + x ^{8} - x ^{4} + 1 ) ( x ^{2} + 1 ) ( x ^{24} - x ^{22} + x ^{20} - x ^{18} + x ^{16} - x ^{14} + x ^{12} - x ^{10} + x ^{8} - x ^{6} + x ^{4} - x ^{2} + 1 ) ( x + 1 ) ( x ^{12} - x ^{11} + x ^{10} - x ^{9} + x ^{8} - x ^{7} + x ^{6} - x ^{5} + x ^{4} - x ^{3} + x ^{2} - x + 1 ) ( x - 1 ) ( x ^{12} + x ^{11} + x ^{10} + x ^{9} + x ^{8} + x ^{7} + x ^{6} + x ^{5} + x ^{4} + x ^{3} + x ^{2} + x + 1 ) ( x ^{416} + x ^{208} + 1 )}{x - 1}

Cancel the common factor:

x - 1

= (x^{8} + 1) (x^{96} - x^{88} + x^{80} - x^{72} + x^{64} - x^{56} + x^{48} - x^{40} + x^{32} - x^{24} + x^{16} - x^{8} + 1) (x^{4} + 1) (x^{48} - x^{44} + x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1) (x^{2} + 1) (x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1) (x + 1) (x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1) (x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1) (x^{416} + x^{208} + 1)

(\frac{ln ( 40 )}{ln ( 5 )}) - 4

x + 1 + \frac{1}{x}

\frac{d}{d t} ((x) (sin (2 t)))

A x^{3} e^{- 2 x} + B x^{2} e^{- 2 x}

\frac{x}{x + 1 - 1}