Resposta :
I) x + 1 = 0 .:. x = -1 (Raiz do Polinômio)
II) x +2 = 0 .:. x = -2 (Raiz do Polinômio)
III) Teorema do Resto P(x) = 0
IV) (-1)^{6} + m (-1)^{4} + n (-1)^{3} -3.(-1) -2 = 0
1 + m -n + 3 -2 = 0 m - n = - 2 , logo n = m+2
V) [tex](-2)^{6} + m (-2)^{4} + n (-2)^{3} -3.(-2) -2 = 0
64 + 16m- 8n- 2 + 6 = 0
16 m - 8 n = -68
16 m - 8(m+2)= - 68
16 m - 8m - 16 = -68
8 m = - 68 +16
8m = -52
m=\frac{-13}{2} [/tex]
Agora é só substituir:
N= m +2
n = [tex] \frac{-13}{2} [/tex] +2
n = [tex] \frac{-13+4}{2} [/tex]
n = [tex] \frac{-9}{2} [/tex]
II) x +2 = 0 .:. x = -2 (Raiz do Polinômio)
III) Teorema do Resto P(x) = 0
IV) (-1)^{6} + m (-1)^{4} + n (-1)^{3} -3.(-1) -2 = 0
1 + m -n + 3 -2 = 0 m - n = - 2 , logo n = m+2
V) [tex](-2)^{6} + m (-2)^{4} + n (-2)^{3} -3.(-2) -2 = 0
64 + 16m- 8n- 2 + 6 = 0
16 m - 8 n = -68
16 m - 8(m+2)= - 68
16 m - 8m - 16 = -68
8 m = - 68 +16
8m = -52
m=\frac{-13}{2} [/tex]
Agora é só substituir:
N= m +2
n = [tex] \frac{-13}{2} [/tex] +2
n = [tex] \frac{-13+4}{2} [/tex]
n = [tex] \frac{-9}{2} [/tex]