There are many ways. The method of dead calculation is to set another factor as cx+d and use the undetermined coefficient method.

(X^2-4X+6)*(cX+d)=x^3+aX^2+bX-6

Then the coefficients are equal respectively.

Get c= 1, d=-1, a=d-4c= -5, b=6c-4d= 10.

Or you can directly divide polynomials by given factors to get binary linear equations about A and B, and then solve them.