Bài giải:

Ta có: P(x) = ${{x}^{5}}+2{{x}^{3}}-4{{x}^{3}}+{{x}^{2}}+4x+9$

P(x) = ${{x}^{5}}+(2{{x}^{3}}-4{{x}^{3}})+{{x}^{2}}+4x+9$

P(x) = ${{x}^{5}}-2{{x}^{3}}+{{x}^{2}}+4x+9$

Q(x) = ${{x}^{5}}+9+2{{x}^{2}}-4{{x}^{2}}-2{{x}^{3}}+3x$

Q(x) = ${{x}^{5}}-2{{x}^{3}}+(2{{x}^{2}}-4{{x}^{2}})+3x+9$

Q(x) = ${{x}^{5}}-2{{x}^{3}}-2{{x}^{2}}+3x+9$

H(x) = P(x) – Q(x) = (${{x}^{5}}-2{{x}^{3}}+{{x}^{2}}+4x+9$) – (${{x}^{5}}-2{{x}^{3}}-2{{x}^{2}}+3x+9$)

= ${{x}^{5}}-2{{x}^{3}}+{{x}^{2}}+4x+9-{{x}^{5}}+2{{x}^{3}}+2{{x}^{2}}-3x-9$

= $({{x}^{5}}-{{x}^{5}})+(-2{{x}^{3}}+2{{x}^{3}})+({{x}^{2}}+2{{x}^{2}})+(4x-3x)+(9-9)$

= $3{{x}^{2}}+x$

Vậy đáp án đúng là: A