2x^3 + 3x^2 + x + 1
=2x^3 + 3x^2 + 3x^2 - 3x^2 + x + 1
=2x^3 + 6x^2 - 3x^2 + x + 1
=2(x^3 + 3x^2) - 3x^2 + x + 1
=2x^2(x+3) - 3x^2 -9x + 9x + x +1
=2x^2(x+3) - 3x(x+3) + 10x +1
=2x^2(x+3) - 3x(x+3) + 10x + 30 - 30 +1
=2x^2(x+3) - 3x(x+3) +10(x+3) -29
The first three terms can be divided by (x+3) evenly so the remainder is -29