x -10
x2+4x+3 ) x3 -6x2+11x -6
x3+4x2 +3x
-10x2 +8x -6
-10x2-40x-30
48x+24 remainder.
(x3-6x2+11x-6)/(x2+4x+3)=x-10 remainder 48x+24.
To prove the divisibility process, multiply x2+4x+3 by x-10=x3+4x2+3x-10(x2+4x+3)=
x3+4x2+3x-10x2-40x-30=x3-6x2-37x-30. Now we have to add the remainder:
x3-6x2-37x-30+(48x+24)=x3-6x2-37x+48x-30+24=x3-6x2+11x-6, the original dividend.