Engage students with this interactive Synthetic Division Maze, where solving polynomial division problems reveals the correct path to the finish.

The image shows a "Synthetic Division Maze" worksheet. The task is to solve synthetic division problems and use the answers to navigate through the maze from "START HERE!" to "FINISHED!". Below, I will explain how to solve one of the synthetic division problems and guide you through the process.

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Step 1: Understand Synthetic Division

Synthetic division is a shorthand method for dividing a polynomial by a binomial of the form \( x - c \). Here's the general process:
1. Write down the coefficients of the dividend polynomial.
2. Use the root \( c \) (from \( x - c \)) in the synthetic division process.
3. Perform the synthetic division steps:
- Bring down the leading coefficient.
- Multiply the root by the number just brought down or calculated.
- Add the result to the next coefficient.
- Repeat until all coefficients are processed.
4. The final row gives the quotient and remainder.

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Step 2: Solve One Example Problem

Let's solve the first problem in the maze:
\[
(x^3 - 6x^2 + 9) \div (x - 4)
\]

#### Step 2.1: Set Up the Problem
- Dividend: \( x^3 - 6x^2 + 0x + 9 \) (Note: Include a placeholder \( 0x \) for the missing \( x \)-term).
- Divisor: \( x - 4 \), so \( c = 4 \).

Coefficients of the dividend: \( 1, -6, 0, 9 \).

#### Step 2.2: Perform Synthetic Division
```
4 | 1 -6 0 9
| 4 -8 -32
-------------------
1 -2 -8 -23
```
- Bring down the first coefficient: \( 1 \).
- Multiply \( 4 \times 1 = 4 \), add to \(-6\): \( -6 + 4 = -2 \).
- Multiply \( 4 \times -2 = -8 \), add to \( 0 \): \( 0 + (-8) = -8 \).
- Multiply \( 4 \times -8 = -32 \), add to \( 9 \): \( 9 + (-32) = -23 \).

#### Step 2.3: Interpret the Results
- The numbers in the bottom row, except the last one, represent the coefficients of the quotient.
- The last number is the remainder.

Quotient: \( x^2 - 2x - 8 \)
Remainder: \(-23\)

So, the result is:
\[
(x^3 - 6x^2 + 9) \div (x - 4) = x^2 - 2x - 8 \text{ R } -23
\]

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Step 3: Navigate the Maze

The answer to the first problem is \( x^2 - 2x - 8 \). Look for this answer in the maze to determine the next step. Follow the path indicated by correct answers until you reach "FINISHED!".

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Step 4: Solve Additional Problems as Needed

Repeat the synthetic division process for each problem you encounter along the path. Use the answers to guide you through the maze.

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Final Answer

The solution involves solving each synthetic division problem and using the answers to navigate the maze. The path will lead you from "START HERE!" to "FINISHED!".

\[
\boxed{\text{Follow the path using correct synthetic division answers.}}
\]