h)
P(x) tiene grado 3
( f(x) es propia
Q(x) tiene grado 6
(x3-x2+x+B=Ax(x2-4x+4)+B(x3+3x)(x3+3x)(x2-4x+4)+C(x2+6x+9)(x2-4x+4)x+ Dx(x3+9x2+27x+27+E(x3+9x2+27x+27)(x2-2x)+F(x3+9x2+27x+27)(x+2-4x+4)x3-x2+x+3=Ax3-4Ax2+4Ax+B(x4-4x3+4x3+3x3-12x3+12x)+xC(x4-4x3+4x2+6x3-24x2+ 24x+9x2-36x+36)+(Dx4+9Dx3+270x2+270x)+E(x5+9x4+27x3+27x2-2x4-18x3-54x2-54x)+F(x5+9x4+27x3+27x2-4x4-36x3-108x2-108x+4x3+36x2 +108x+108)
x3-x2+x+3=Ax3-4Ax3+4Ax+B(x4-x3-8x2+12x)+C(x5-2x4-11x3-12x2+36x)+
(Dx4+90x3+27Dx2+27Dx)+E(x5+7x4+9x3-27x2-54)+F(x5+5x4-5x3-45x2+108)x3-x2+x+3=x5(C+E+F)+x4(B-2C+D+7E+5F)+x3(A-B-11C+9D+9E-5F)+x2(-4-8B-12C
+27D-27E-45F)+x(4+12B+36C+27D)+(-54E+108F)
C+E+F= 0 = E+F=-C
B-2C+D+7E+5F=0
A-B-11C+9D+9E-5F=1
(-4A-8B-12C+27D-27E-45F=1
4+12B+36C+27D=1
-54E+108F=3
-18E+36F=1
-18(E-2F)=1
-E+2f=
4A-4B-44C+36D+36E-20F=4
4B+24C+54D-27E-45F=2
B- 2C+ D- 7E+ 5F=0 x-4
32C+ 5D+ E-65F=232 (-E-F) + 5D + E -65F = 2
-31E 97F + 5D = 2
31-9F+5D=2 ( -71F + 5D = 2
5D-71F=2-
5D-71F=
E + F = - C (2F -+F=-C50-71F=
3F + C =
- E + 2F =
B -
B 2C + D + 7E + 5F = 0
B 2(-E-F)+-+7+5F=0
B 2
B-4F+
B 59F =
B 59F =
4A+12
4A+8+
4A+
4A+
4A+
M. PARCIALEC
m)
(x4+5x2+4 = (x2+1)(x2+4)
2 x 5x2 = (Ax3 + 4Ax + Bx2 + 4B) + (Cx3 + CX + Dx2 + D)
2 x 5x2 = x3 (A + C) + x2 (B+D) + x(4A + C) + (4B + D)
A + C = 0
A + C = 0
B + D = -5 (-B + D = - 5 ( D = 4A + C = - 1
4B + D = 2
4A + C = - 1
-3A = 1
-3B = -7 ( B =
4B + D = 2
A =
( 4 . -
=
=
=
=
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