Divide the following polynomials, then place the answer in the proper location on the grid. write answer in descending powers of x. (4x3 + 3x2 - 30x - 10) ÷ (x -3)

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