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DESCARGA

CAPITULO X

Descomposición Factorial

Ejercicio 89

Factorar o descomponer en dos factores:

$a^{2} + a b = a (a + b)$
$b + b^{2} = b (1 + b)$
$x^{2} + x = x (x + 1)$
$3 a^{3} - a^{2} = a^{2} (3 a - 1)$
$x^{3} - 4 x^{4} = x^{3} (1 - 4 x)$
$5 m^{2} + 15 m^{3} = 5 m^{2} (1 + 3 m)$
$a b + b c = b (a + c)$
$x^{2} y + x^{2} z = x^{2} (y + z)$
$2 a^{2} x + 6 a x^{2} = 2 a x (a + 3 x)$
$8 m^{2} - 12 m n = 4 m (2 m - 3 n)$
$9 a^{3} x^{2} - 18 a x^{3} = 9 a x^{2} (a - 2 x)$
$15 c^{3} d^{2} + 60 c^{2} d^{3} = 15 c^{2} d^{2} (c + 4 d)$
$35 m^{2} n^{3} - 70 m^{3} = 35 m^{2} (n^{3} - 2 m)$
$a b c + a b c^{2} = a b c (1 + c)$
$24 a^{2} x y^{2} - 36 x^{2} y^{4} = 12 x y^{2} (2 a^{2} - 3 x y^{2})$
$a^{3} + a^{2} + a = a (a^{2} + a + 1)$
$4 x^{2} - 8 x + 2 = 2 (2 x^{2} - 4 x + 1)$
$15 y^{3} + 20 y^{2} - 5 y = 5 y (3 y^{2} + 4 y - 1)$
$a^{3} - a^{2} x + a x^{2} = a (a^{2} - a x + x^{2})$
$2 a^{2} x + 2 a x^{2} - 3 a x = a x (2 a + 2 x - 3)$
$x^{3} + x^{5} - x^{7} = x^{3} (1 + x^{2} - x^{4})$
$14 x^{2} y^{2} - 28 x^{3} + 56 x^{4} = 14 x^{2} (y^{2} - 2 x + 4 x^{2})$
$34 a x^{2} + 51 a^{2} y - 68 a y^{2} = 17 a (2 x^{2} + 3 a y - 4 y^{2})$
$96 - 48 m n^{2} + 144 n^{3} = 48 (2 - m n^{2} + 3 n^{3})$
$a^{2} b^{2} c^{2} - a^{2} c^{2} x^{2} + a^{2} c^{2} y^{2} = a^{2} c^{2} (b^{2} - x^{2} + y^{2})$
$55 m^{2} n^{3} x + 110 m^{2} n^{3} x^{2} - 220 m^{2} y^{3} = 55 m^{2} (n^{3} x + 2 n^{3} x^{2} - 4 y^{3})$
$93 a^{3} x^{2} y - 62 a^{2} x^{3} y^{2} - 124 a^{2} x = 31 a^{2} x (3 a x y - 2 x^{2} y^{2} - 4)$
$x - x^{2} + x^{3} - x^{4} = x (1 - x + x^{2} - x^{3})$
$a^{6} - 3 a^{4} + 8 a^{3} - 4 a^{2} = a^{2} (a^{4} - 3 a^{2} + 8 a - 4)$
$25 x^{7} - 10 x^{5} + 15 x^{3} - 5 x^{2} = 5 x^{2} (5 x^{5} - 2 x^{3} + 3 x - 1)$
$x^{15} - x^{12} + 2 x^{9} - 3 x^{6} = x^{6} (x^{9} - x^{6} + 2 x^{3} - 3)$
$9 a^{2} - 12 a b + 15 a^{3} b^{2} - 24 a b^{3} = 3 a (3 a - 4 b + 5 a^{2} b^{2} - 8 b^{3})$
$16 x^{3} y^{2} - 8 x^{2} y - 24 x^{4} y^{2} - 40 x^{2} y^{3} = 8 x^{2} y (2 x y - 1 - 3 x^{2} y - 5 y)$
$12 m^{2} n + 24 m^{3} n^{2} - 36 m^{4} n^{3} + 48 m^{5} n^{4} = 12 m^{2} n (1 + 2 m n - 3 m^{2} n^{2} + 4 m^{3} n^{3})$
$100 a^{2} b^{3} c - 150 a b^{2} c^{2} + 50 a b^{3} c^{3} - 200 a b c^{2} = 50 a b c (2 a b^{2} - 3 b c^{2} + b^{2} c^{2} - 4 c^{2})$
$x^{5} - x^{4} + x^{3} - x^{2} + x = x (x^{4} - x^{3} + x^{2} - x + 1)$
$a^{2} - 2 a^{3} + 3 a^{4} - 4 a^{5} + 6 a^{6} = a^{2} (1 - 2 a + 3 a^{2} - 4 a^{3} + 6 a^{4})$
$3 a^{2} b + 6 a b - 5 a^{3} b^{2} + 8 a^{2} b x + 4 a b^{2} m = a b (3 a + 6 - 5 a^{2} b + 8 a x + 4 b m)$
$a^{20} - a^{16} + a^{12} - a^{8} + a^{4} - a^{2} = a^{2} (a^{18} - a^{14} + a^{10} - a^{6} + a^{2} - 1)$