There are several methods to solve here.
You could expand out and set equal to P(x), equate coefficients and solve the system.
An easier way is to set x equal to the respective amounts which will result in 0. Like so:
Use 1, 2, 3
\(\displaystyle A+B(1-1)+C(1-1)(1-2)+D(1-1)(1-2)(1-3)=3(1)^{3}+2(1)^{2}+(1)+5\)
\(\displaystyle A+B(2-1)+C(2-1)(2-2)+D(2-1)(2-2)(2-3)=3(2)^{3}+2(2)^{2}+(2)+5\)
Do the same thing for 3, You will then have a system involving A, B, C
Your system should look like:
A=11
A+B=39
A+2B+2C=107
After you have these three values, then you need to enter in your known values and find D.
