Is this a short way of doing the question:Let$\displaystyle P_1=x^3-3x-2$ and $\displaystyle P_2=x^4+x^3+2x^2+5x+3$. Find $\displaystyle hcf (P_1, P_2).$

$\displaystyle P_1(x)=x^3-3x-2=(x+1)^2(x-2)$

$\displaystyle P_2(x)=x^4+x^3+2x^2+5x+3=(x+1)^2(x^2-x+3)$

Hence $\displaystyle hcf(P_1,P_2)=(x+1)^2.$