Ответ: 2x²-7x+3.

Объяснение:

[tex]\displaystyle\\2x^3-9x^2+10x-3=(x-1)(ax^2+bx+c)=ax^3+bx^2+cx-ax^2-bx-c=\\\\=ax^3+(b-a)x^2+(c-b)x-c.\ \ \ \ \ \ \ \ \Rightarrow\\\\\left\{\begin{array}{cccc}a=2\\b-a=-9\\c-b=10\\-c=-3\ |*(-1)\end{array}\right \ \ \ \ \ \ \ \ \ \ \left\{\begin{array}{ccc}a=2\\b=-7\\c=3\end{array}\right\ \ \ \ \ \ \ \ \Rightarrow\\\\\\\\\frac{2x^3-9x^2+10x-3}{x-1}=\frac{(x-1)(2x^2-7x+3)}{x-1}=2x^2-7x+3. \\[/tex]