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,
x+3
+-8, +-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