Use synthetic division to find the result when 2x^4+x^3-13x^2-27x+9 is divided by x-3 Answer Attempt 1out of 3 square

To use synthetic division to divide the polynomial \(2x^4 + x^3 - 13x^2 - 27x + 9\) by \(x - 3\), we follow these steps:<br /><br />1. Write down the coefficients of the polynomial: \(2, 1, -13, -27, 9\).<br />2. Write the value that makes the divisor zero (which is \(3\)) to the left.<br />3. Bring down the first coefficient (which is \(2\)).<br />4. Multiply the value just written below the line by the value to the left, and write the result in the next column.<br />5. Add the value in the next column to the value above it, and write the result below the line.<br />6. Repeat steps 4 and 5 until all columns are filled.<br /><br />Here is the synthetic division setup and process:<br /><br />\[<br />\begin{array}{r|rrrrr}<br />3 & 2 & 1 & -13 & -27 & 9 \\<br /> & & 6 & 21 & 24 & -9 \\<br />\hline<br /> & 2 & 7 & 8 & -3 & 0 \\<br />\end{array}<br />\]<br /><br />Explanation of each step:<br />- The first row contains the coefficients of the polynomial.<br />- The second row is used to perform the synthetic division.<br />- The third row contains the results after each operation.<br /><br />The final row gives the coefficients of the quotient polynomial and the remainder. Since the remainder is \(0\), the quotient polynomial is \(2x^3 + 7x^2 + 8x - 3\).<br /><br />Thus, the result of dividing \(2x^4 + x^3 - 13x^2 - 27x + 9\) by \(x - 3\) using synthetic division is:<br /><br />\[<br />2x^3 + 7x^2 + 8x - 3<br />\]