divide xcube - 6xsquare+11x -6 by xsquare+4x+3 and also verify the division algorithm

Question

nothing more information

Answer 1

                  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.