Question

If P(x)=3x^3+2x^2+x+14 and we write P(x) in the form P(x)=A+B(x-1)+C(x-1)(x-2)+D(x-1)(x-2)(x-3) , what are the values of A and B ?

How to start to find A and B?

Answer 1

Make C and D vanish.

Answer 2

Try plugging in x=1 and x=2 in P(x)=A+B(x-1)+C(x-1)(x-2)+D(x-1)(x-2)(x-3).