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DESCARGA

CAPITULO X

Descomposición Factorial

Ejercicio 105

Factorar:

$a^{5} + 1 = (a + 1) (a^{4} - a^{3} + a^{2} - a + 1)$
$a^{5} - 1 = (a - 1) (a^{4} + a^{3} + a^{2} + a + 1)$
$1 - x^{5} = (1 - x) (1 + x + x^{2} + x^{3} + x^{4})$
$a^{7} + b^{7} = (a + b) (a^{6} - a^{5} b + a^{4} b^{2} - a^{3} b^{3} + a^{2} b^{4} - a b^{5} + b^{6})$
$m^{7} - n^{7} = (m - n) (m^{6} + m^{5} n + m^{4} n^{2} + m^{3} n^{3} + m^{2} n^{4} + m n^{5} + n^{6})$
$a^{5} + 243 = (a + 3) (a^{4} - 3 a^{3} + 9 a^{2} - 27 a + 81)$
$32 - m^{5} = (2 - m) (16 + 8 m + 4 m^{2} + 2 m^{3} + m^{4})$
$1 + 243 x^{5} = (1 + 3 x) (1 - 3 x + 9 x^{2} - 27 x^{3} + 81 x^{4})$
$x^{7} + 128 = (x + 2) (x^{6} - 2 x^{5} + 4 x^{4} - 8 x^{3} + 16 x^{2} - 32 x + 64)$
$243 - 32 b^{5} = (3 - 2 b) (81 + 54 b + 36 b^{2} + 24 b^{3} + 16 b^{4})$
$a^{5} + b^{5} c^{5} = (a + b c) (a^{4} - a^{3} b c + a^{2} b^{2} c^{2} - a b^{3} c^{3} + b^{4} c^{4})$
$m^{7} - a^{7} x^{7} = (m - a x) (m^{6} + m^{5} a x + m^{4} a^{2} x^{2} + m^{3} a^{3} x^{3} + m^{2} a^{4} x^{4} + m a^{5} x^{5} + a^{6} x^{6})$
$1 + x^{7} = (1 + x) (1 - x + x^{2} - x^{3} + x^{4} - x^{5} + x^{6})$
$x^{7} - y^{7} = (x - y) (x^{6} + x^{5} y + x^{4} y^{2} + x^{3} y^{3} + x^{2} y^{4} + x y^{5} + y^{6})$
$a^{7} + 2187 = (a + 3) (a^{6} - 3 a^{5} + 9 a^{4} - 27 a^{3} + 81 a^{2} - 243 a + 729)$
$1 - 128 a^{7} = (1 - 2 a) (1 + 2 a + 4 a^{2} + 8 a^{3} + 16 a^{4} + 32 a^{5} + 64 a^{6})$
$x^{10} + 32 y^{5} = (x^{2} + 2 y) (x^{8} - 2 x^{6} y + 4 x^{4} y^{2} - 8 x^{2} y^{3} + 16 y^{4})$
$1 + 128 x^{14} = (1 + 2 x^{2}) (1 - 2 x^{2} + 4 x^{4} - 8 x^{6} + 16 x^{8} - 32 x^{10} + 64 x^{12})$