Use synthetic division to divide. (x^2+5x-36)/(x+9) __ (x^2+5x-36)/(x+9)= square

To use synthetic division to divide \(\frac{x^2 + 5x - 36}{x + 9}\), we first need to rewrite the divisor \(x + 9\) in the form \(x - c\). We can do this by setting \(x + 9 = 0\), which gives us \(x = -9\). So, we will use \(c = -9\) for synthetic division.<br /><br />The coefficients of the polynomial \(x^2 + 5x - 36\) are \(1, 5, -36\).<br /><br />Now, we set up the synthetic division:<br /><br />\[<br />\begin{array}{r|rrr}<br />-9 & 1 & 5 & -36 \\<br /> & & -9 & 36 \\<br />\hline<br /> & 1 & -4 & 0 \\<br />\end{array}<br />\]<br /><br />Here's the step-by-step process:<br /><br />1. Bring down the first coefficient (1).<br />2. Multiply -9 by the value just written below the line (1), which gives -9. Write this under the next coefficient (5).<br />3. Add the values in the second column: \(5 + (-9) = -4\). Write this result below the line.<br />4. Multiply -9 by the value just written below the line (-4), which gives 36. Write this under the next coefficient (-36).<br />5. Add the values in the third column: \(-36 + 36 = 0\). Write this result below the line.<br /><br />The final row gives us the coefficients of the quotient polynomial. Since the remainder is 0, the quotient polynomial is \(x - 4\).<br /><br />Therefore, \(\frac{x^2 + 5x - 36}{x + 9} = x - 4\).