X³+0x²+3x+6÷ by 3x-2 find the remainder

y= - 271/71

x=755/71

z =4866/71

Step-by-step explanation:

For resolve a system you multiply an equation of the system or add two of the equation and replace the result in the system

                                                     Add the 1st and 2nd, and replace the 2nd

4x + 3y + z= -6         4x + 3y + z= -6          4x + 3y + z= -6

(-4) (x-3y + 2z=0 ) → -4x +12y -8z =0      →       +15y -7z = -6

11x-2y + 3z = - 26    11x-2y + 3z = - 26       11x-2y + 3z = - 26

                                                      Add the 2nd and 1st, and replace the 1st

4x + 3y + z= -6          4x + 3y + z= -6                    4x  + z= -6

(-1/5)( 15y -7z = -6) →  -3y -7/5z =6/5      →       -3y -7/5z =6/5

11x-2y + 3z = - 26     11x-2y + 3z = - 26           11x-2y + 3z = - 26

                                                      Add the1st and 3rd, and replace the 3erd

(-3)( 4x  + z= -6)          -12x - 3z= 18                    -12x - 3z= 18

-3y -7/5z =6/5      →  -3y -7/5z =6/5      →       -3y -7/5z =6/5

11x-2y + 3z = - 26      11x-2y + 3z = - 26           -x-2y  = - 8

                                                       Add the1st and 3rd, and replace the 1st

(1/3)(-12x - 3z= 18 )     -4x - z= 6                 -4x - z= 6

(5)(-3y -7/5z =6/5) →  -15y - 7z = 6        → -15y - 7z = 6

-x-2y  = - 8               (-4)(-x-2y  = - 8)         4x + 8y= 32

                          Add the 1st and 2nd, and replace the 2nd

(-7)(8y - z =38)        -56y +7z= 266     -56y +7z= 266

-15y - 7z = 6     →     -15y - 7z = 6  →      -71y=271 → y= - 271/71

(1/4)(4x + 8y= 12)       x+2y=3                 x+2y=3

-56y +7z= 266 → -8y + z =38 → z =4866/71

x+2y=3 → x=755/71