Is it always true that a line connecting two points on the same side of given line will be parallel to that given line?

No, its not always true

It is possible to have a parallel line form, but you could easily have the new line intersect the old one. It depends on how you place the points.

Side note: Parallel lines have equal slopes but different y intercepts.

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."