Use synthetic division to divide the polynomial ? 6 x 3 ? 4 + 7 x + 11 by the polynomial x ? 6 Fill in the synthetic division table Therefore, the resulting polynomial is with a remainder of

We set up the synthetic division table as follows: 6 | -6 0 7 11 |______-36__-216__-1629 -6 | -6 -36 -209 -1618 The coefficients of the dividend, -6, 0, 7, and 11, are entered in the top row of the table. The divisor, x - 6, is written to the left of the table with its constant term, 6, on the outside. The first element in the second row is simply the first coefficient of the dividend, -6. To find the next entry, we multiply the divisor by -6, which gives us -36. We add this value to the second coefficient of the dividend, 0, and write the result in the second column of the table. This process is repeated for the third coefficient of the dividend, 7. We obtain -209 by multiplying the divisor by -36 and adding it to 7. Finally, we repeat the process for the last coefficient of the dividend, 11, and get -1618. The last number in the second row, -1618, is the remainder. The polynomial resulting from the division is the coefficients in the third row, which gives us -6, -36, -209, and -1618. Thus, the resulting polynomial is: -6x^2 - 36x - 209 with a remainder of -1618.