Cho đa thức F(x) = x^7 – 1/2x^3 + x + 1. a) Tìm đa thức Q(x) sao cho F(x) + Q(x) = x^5 – x^3 + 2.

a) Ta có: F(x) + Q(x) = x⁵ – x³ + 2.

Suy ra Q(x) = x⁵ – x³ + 2 – F(x)

Hay Q(x) = x⁵ – x³ + 2 – (x⁷ – 12x³ + x + 1)

                = x⁵ – x³ + 2 – x⁷ + 12x³ – x – 1

                = – x⁷ + x⁵ + (– x³ + 12x³) – x + (2 – 1)

                = – x⁷ + x⁵ – 12x³ – x + 1.

Vậy Q(x) = – x⁷ + x⁵ – 12x³ – x + 1.