a) Ta có: $F(x)+Q(x)=x^{5}-x^{3}+2$.
Suy ra $Q(x) =x^{5}-x^{3}+2 - F(x) = x^{5}-x^{3}+2 -(x^{7} -\frac{1}{2}x^{3}+x+1)$
$= x^{5}-x^{3}+2 -x^{7}+\frac{1}{2}x^{3}-x-1=-x^{7}+x^{5}-\frac{1}{2}x^{3}-x+1$
Vậy Q(x) = $-x^{7}+x^{5}-\frac{1}{2}x^{3}-x+1$
b) Ta có F(x) - R(x) = 2.
Suy ra R(x) = F(x) - 2 = $x^{7}-\frac{1}{2}x^{3}+x+1-2=x^{7}-\frac{1}{2}x^{3}+x-1$