Remainder theorem question

Question

If the polynomials x^4 + 3x^3 + 2x^2 + ax + b and x^3 + 3x^2 - 5x + 6 have the same remainder when divided by (x+1)^2, find the value of a and b

Answer 1

First, I did a long division on the polynominal with all coefficients and got a remainder of -8x+5

Then did a long division for the polynomial with unknown coefficients and got a remainder (a+1)x+(b+1)

 

Then set -8=a+1 and 5=b+1 and solved for a and b and got a=-9 and b=4

 

Then, just to be sure, I checked the answer by doing the long division with the values for a and b and I got the same remainders.