Find an explicit formula for the arithmetic sequence
81,54,27,0,...

an = -27n + 108.

Step-by-step explanation:

The first term a1 = 81 and the common difference d = 54-81 = -27 . (Also 27 - 54 = -27 and 0 - 27 = -27).

The explicit formula is  

an = a1 + d(n - 1)

= 81 - 27(n - 1)

= -27n + 81 + 27

= -27n + 108.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."