Question

6. ¿Cuáles son las características del siguiente polinomio -2x5 – x4 + 14x3 + 16x2 – x + 3?

Answer 1

P(x) + Q(x) - R(x) = = (x4 -2x2 - 6x - 1) + (x3 - 6x2 + 4) - ( 2x4 -2 x - 2) = = x4 -2x2 - 6x - 1 + x3 - 6x2 + 4 - 2x4 + 2 x + 2 = = x4 - 2x4 + x3 -2x2 - 6x2 - 6x + 2 x - 1 + 4 + 2 = = -x4 + x3 - 8x2 - 4x + 5 P(x) + 2 Q(x) - R(x) = =(x4 -2x2 - 6x - 1) + 2(x3 - 6x2 + 4) - ( 2x4 -2 x - 2) = = x4 -2x2 - 6x - 1 +2x3 - 12x2 + 8 - 2x4 + 2 x + 2 = = x4 - 2x4 + 2x3 -2x2 - 12x2 - 6x + 2 x - 1 + 8 + 2 = = -x4 + 2x3- 14x2 - 4x + 9 Q(x)+ R(x) - P(x)= = (x3 - 6x2 + 4) + ( 2x4 -2 x - 2) - (x4 -2x2 - 6x - 1) = = x3 - 6x2 + 4 + 2x4 -2 x - 2 - x4 +2x2 + 6x + 1= = 2x4 - x4 + x3 - 6x2 +2x2 -2 x + 6x + 4- 2 + 1= = x4 + x3 - 4x2 + 4x + 3 1(x4 -2x2 +2 ) · (x2 -2x +3) = = x 6 -2x5 + 3x4 - 2x4 + 4x3 - 6x2 + 2x2- 4x +6= = x 6 -2x5 - 2x4 + 3x4 + 4x3 + 2x2 - 6x2 - 4x +6 = = x 6 -2x5 + x4 + 4x3 - 4x2 - 4x + 6 2 (3x2 - 5x ) · (2x3 + 4x2 - x +2) = = 6x5 + 12x4 - 3x3 + 6x2 - 10x4 - 20x3 + 5x2 - 10x = = 6x5 + 12x4 - 10x4 - 3x3 - 20x3 + 6x2 + 5x2 - 10x = = 6x5 + 2x4 - 23x3 + 11x2 - 10x 3 (2x2 - 5x + 6) · (3x4 - 5 x3 - 6 x2 + 4x - 3) = = 6x6 - 10x5 - 12 x4 + 8x3 - 6 x2 - - 15x5 + 25x4 + 30x3 - 20x2+ 15x + +18x4 - 30x3 - 36x2 + 24x - 18 = = 6x6 - 10x5 - 15x5 - 12 x4 + 25x4 + 18x4 + +8x3 - 30x3 + 30x3- 6 x2- 20x2 - 36x2 + 15x + 24x - 18 = = 6x6 - 25x5 + 31x4 + 8x3 - 62x2 + 39x - 18