Let $H(x)=3 x^4+6 x^3-2 x^2+1$ and $g(x)$ be a linear polynomial. If $\frac{H(x)}{(x-1)(x+1)(x-2)}=f(x)+\frac{g(x)}{(x-1)(x+1)(x-2)}$, then $H(-1)+2 H(2)-3 H(1)=$

• A

  $f(-1)+2 f(2)-3 f(1)$
• B

  $\mathrm{H}(-1)+\mathrm{f}(2)+\mathrm{g}(3)$
• Correct answer
  C

  $g(-1)+2 g(2)-3 g(1)$
• D

  $\mathrm{H}(1)+2 \mathrm{f}(2)-\mathrm{g}(1)$

Hence, the correct answer is option: 'C'.