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Let's solve the problem using **synthetic division**.

We are tasked with dividing:

\[
2x^3 - 6x^2 + 0x - 5
\]

by:

\[
x - 1
\]

### Step-by-step process:

1. **Set up the synthetic division**:
   - The divisor is \(x - 1\), so we use \(1\) (the zero of \(x - 1\)) as the number for synthetic division.
   - The coefficients of the polynomial \(2x^3 - 6x^2 + 0x - 5\) are \(2\), \(-6\), \(0\), and \(-5\).

   We now create the synthetic division setup:

   \[
   \begin{array}{r|rrrr}
   1 & 2 & -6 & 0 & -5 \\
   \end{array}
   \]

2. **Perform synthetic division**:
   - Bring down the first coefficient (2) directly under the line.
   - Multiply \(2\) by \(1\) and write the result under the next coefficient.
   - Add \(-6 + 2 = -4\), and continue the process.

   Here is the synthetic division table as we proceed:

   \[
   \begin{array}{r|rrrr}
   1 & 2 & -6 & 0 & -5 \\
     &   & 2 & -4 & -4 \\
   \hline
     & 2 & -4 & -4 & -9 \\
   \end{array}
   \]

3. **Interpret the result**:
   - The bottom row gives us the coefficients of the quotient and remainder.
   - The quotient is \(2x^2 - 4x - 4\), and the remainder is \(-9\).

4. **Write the final answer**:
   - Using the form \(\frac{q(x) + \frac{r(x)}{d(x)}}\), where:
     - \(q(x) = 2x^2 - 4x - 4\),
     - \(r(x) = -9\),
     - \(d(x) = x - 1\),

   The final answer is:

   \[
   2x^2 - 4x - 4 - \frac{9}{x - 1}
   \]

Would you like more details on any step? 

Here are 5 questions that build on this concept:
1. How does synthetic division differ from long division in polynomials?
2. Can synthetic division be used if the divisor is \(x + 1\)?
3. What would happen if the remainder were zero in this process?
4. How can you verify the result of synthetic division by multiplying?
5. How does synthetic division help when solving rational expressions?

**Tip**: Always remember to include the placeholder \(0\) for any missing terms in the polynomial.

Use synthetic division to divide 2x^3 - 6x^2 - 5 by x - 1.

Learn how to use synthetic division to divide the polynomial 2x^3 - 6x^2 - 5 by x - 1. This step-by-step solution covers important algebraic concepts related to polynomial division, including quotient and remainder determination.

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