Example

(x-3) is a factor of f(x)=3x^3-7x^2-5x-3.

So (x-3) is a factor of 3x^3-7x^2-5x-3=(x-3)(bx^2+cx+d).

a=3, b=3,c=2,d=1

I want to clarify my understanding of the below:

a=3 from 3x^3???

considering coefficient x^3 gives b=3....from 3x^3???

considering coefficient x^0 gives -3=-3d..:.d=1. from -3)+d)??? ie the last term??.

considering coefficient x^2 gives -7=c-3b.:.c=2....why c-3b???