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Factorización aplicando Ruffini o Método de Evaluación
1.
Factorizar aplicando Ruffini 1.)
x3 + 5x2 - 2x – 24 = (x–2)(x+3)(x+4) SOLUCION x-2 Divisores del Termino Independiente (-24): 1, 2, 4, 6, 8, x+3 12, 24 x2 - 2x x3 x2 x I 3x - 6 1 5 -2 -24 x2 + x - 6 2 2 14 24 x+4 1 7 12 0 → x= 2 = x-2 = 0 x3 + x2 - 6x -3 -3 -12 4x2 + 4x - 24 1 4 0 → x= -3 = x+3 = 0 x3 + 5x2 - 2x - 24 -4 -4 1 0 → x= -4 = x+4 = 0 2.) 2x3 – 3x2 – 11x + 6 = (x–½)(x+2)(x-3) = ( 2x - 1 ) ( x + 2 ) ( x - 3 ) Divisores del Termino Independiente (6): 1, 2 3, 6 Divisores del Coeficiente de x3 (2) : 1, 2 SOLUCION Posibles Raíces Fraccionarias: ½, 2/2, 3/2, 6/2 2x – 1 x+2 x3 x2 x I 2x2 – x 2 -3 -11 6 4x - 2 ½ 1 -1 -6 2x2 – 3x - 2 2 -2 -12 0 → x= ½ = x-½ = 0 x-3 -2 -4 12 2x3 + 3x2 – 2x – 6x2 – 9x + 6 2 -6 0 → x= -2 = x+2 = 0 2x3 – 3x2 – 11x + 6 3 6 2 0 → x= 3 = x-3 = 0
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