Altho you could use long division here, synthetic div. is faster (if you know it). If the divisor is x-3, then use 3 as the divisor in long div.:
___________________
3 / 4 3 -30 -10
12 45 45
---------------------------
4 15 15 35
The remainder is 35, not zero, so if you divide 4x^3 + 3x^2 - 30x - 10 by (x-3) you'll get the remainder 35.
The coefficients of the quotient are 4, 15 and 15:
35
4x^2 + 15x + 15 + ------------- (answer)
x-3
