Fill in the blank so that the resulting statement is true. To divide $x^{3}-6 x-5$ by $x+2$ using synthetic division, the first step is to write To divide $x^{3}-6 x-5$ by $x+2$ using synthetic division, the first step is to write
Solution
Step 1 ：The first step in synthetic division is to write down the coefficients of the polynomial we are dividing. In this case, the polynomial is \(x^{3}-6 x-5\). However, we need to be careful to include terms for any missing powers of \(x\). In this case, there is no \(x^2\) or \(x\) term, so we need to include these as 0 in our list of coefficients. Therefore, the coefficients we write down are 1 (for \(x^{3}\)), 0 (for \(x^{2}\)), -6 (for \(x\)), and -5 (for the constant term). We also write down the number we are dividing by, which is -2 (the opposite of the number in \(x+2\)).
Step 2 ：\(\boxed{\text{The first step is to write down the coefficients of the polynomial } x^{3}-6 x-5 \text{ as 1, 0, -6, -5 and the number we are dividing by as -2.}}\)
