What is the next number in the following series: 2, 5, 8, 11, a. 14 b. 13 c. 12 d. 15

There is a pattern that exists here. They go up by increments of 3:

2+3=5; 5+3=8; 8+3=11

If you add 3 to 11, the result is 14. The answer is 14.

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."