divide x92x87x619x533x460x3120x2100 by x3 write the result i

divide x^9+2x^8-7x^6+19x^5-33x^4+60x^3+120x^2-100 by x+3. write the result in DDQR form.

Solution

x+3...]...x⁹+2x⁸+0x⁷-7x⁶+19x⁵-33x⁴+60x³+120x²+0x-100....[x⁸-x⁷+3x⁶-16x⁵+67x⁴-234x³+762x²-2166x+6498
.............x⁹+3x⁸.................
............(-)....(-).................................................
.................-x⁸+0x⁷....................
..................-x⁸-3x⁷....................
...................(+)..(+)............................
...................3x⁷-7x⁶......................
...................3x⁷+9x⁶......................
....................(-).....(-)...........................
........................-16x⁶+19x⁵......................
........................-16x⁶-48x⁵......................
..........................(+)....(+).....................................
.................................67x⁵-33x⁴..................................
................................67x⁵+201x⁴..................................
...................................(-)......(-)......................................
.........................................-234x⁴+60x³.....................
........................................-234x⁴-702x³.....................
...........................................(+).....(+)..........................
....................................................762x³+120x²...........
....................................................762x³+2286x².........
.........................................................(-)........(-)....................
..............................................................-2166x²+0x...........................
..............................................................-2166x²-6498x...........................
.................................................................(+)........(+).............
...........................................................................6498x-100...........................
...........................................................................6498x+19494................
...............................................................................(-).........(-)...................
........................................................................................-19594.....................

divisor:x+3

dividend:x⁹+2x⁸+0x⁷-7x⁶+19x⁵-33x⁴+60x³+120x²+0x-100

quotient:x⁸-x⁷+3x⁶-16x⁵+67x⁴-234x³+762x²-2166x+6498

remainder:-19594

x⁹+2x⁸+0x⁷-7x⁶+19x⁵-33x⁴+60x³+120x²+0x-100

=((x+3)*(x⁸-x⁷+3x⁶-16x⁵+67x⁴-234x³+762x²-2166x+6498))-19594