If $\text{⨍ }\left(\mathrm{x}\right) =2{\mathrm{x}}^4 – 13{\mathrm{x}}^2 + \mathrm{ax} + \mathrm{b}$ is divisible by ${\mathrm{x}}^2 – 3\mathrm{x} +2$, then (a, b)=

$\begin{array}{l}{x}^2-3x+2=x^2-2x-x+2=(x-2)(x-1)\\ Iff\left(x\right)=2x^4-13x^2+ax+bisdivisibleby(x-2)(x-1)\\ Thenf\left(2\right)=0andf\left(1\right)=0\\ \therefore f\left(2\right)=0\Rightarrow 2{\left(2\right)}^4-13{\left(2\right)}^2+2a+b=0\\ \Rightarrow 32-52+2a+b=0\\ \Rightarrow 2a+b=20--\left(1\right)\\ \therefore f\left(1\right)=0\Rightarrow 2{\left(1\right)}^4-13{\left(1\right)}^2+a\left(1\right)+b=0\\ \Rightarrow 2-13+a+b=0\\ \Rightarrow a+b=11--\left(2\right)\\ \left(1\right)-\left(2\right)\Rightarrow a=9\\ from\left(2\right)a+9=11\Rightarrow a=2\\ \therefore (a,b)=(9,2)\end{array}$