(a) Complete this synthetic division table. -5longdiv (-1 -5 4 12) square square square square square square (b) Write your answer in the following form: Quotient+(Remainder)/(x+5) (-x^3-5x^2+4x+12)/(x+5)=square +(square )/(x+5)

(a) To complete the synthetic division table, we need to follow these steps:<br /><br />1. Write down the coefficients of the polynomial: -1, -5, 4, 12.<br />2. Bring down the first coefficient (-1) to the quotient row.<br />3. Multiply the divisor (-5) by the value just written in the quotient row (-1) and write the result (-5) in the next column of the quotient row.<br />4. Add the value just written in the quotient row (-5) to the value in the same column of the dividend5) and write the result (0) in the quotient row.<br />5. Repeat steps 3 and 4 until all columns are filled.<br /><br />The completed synthetic division table should look like this:<br /><br />$-5\longdiv {-1\quad -5\quad 4\quad 12}\\ 5\quad 0\quad 0\\ \hline 1\quad 0\quad 0\quad 0$<br /><br />(b) The quotient is 1 and the remainder is 0. Therefore, the answer in the form of Quotient + Remainder/(x+5) is:<br /><br />$\frac {-x^{3}-5x^{2}+4x+12}{x+5}=1+\frac{0}{x+5}$