Divide. If the polynomial does not divide evenly, include the remainder as a fraction. $$ \left.\qquad 4 u^{2}-14 u+11\right) \div(u-2) $$ Submit

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To divide the polynomial $$4u^{2} - 14u + 11$$ by $$u - 2$$, we can use polynomial long division or synthetic division. Here's the step-by-step process using synthetic division:

### Step 1: Set Up Synthetic Division
- **Divisor root**: For $$u - 2$$, the root is $$u = 2$$.
- **Coefficients** of the dividend $$4u^{2} - 14u + 11$$ are: **4**, **-14**, **11**.

### Step 2: Perform Synthetic Division

$$
\begin{array}{c|ccc}
2 & 4 & -14 & 11 \
\hline
 & & 8 & -12 \
\hline
 & 4 & -6 & -1 \
\end{array}
$$

- **Bring down the 4**.
- **Multiply 4 by 2** (divisor root) to get **8**. Add this to -14 to get **-6**.
- **Multiply -6 by 2** to get **-12**. Add this to 11 to get **-1**.

### Step 3: Write the Result
- The **quotient** is $$4u - 6$$.
- The **remainder** is $$-1$$.

Since the polynomial does not divide evenly, include the remainder as a fraction:

$$
\frac{-1}{u - 2}
$$

### Final Answer:
$$
\boxed{4\,u\ -\ 6\ -\ \dfrac{1}{\,u\!-\!2\,}}
$$
The division of $$4u^{2} - 14u + 11$$ by $$u - 2$$ results in $$4u - 6$$ with a remainder of $$-1$$. Therefore, the final expression is $$4u - 6 - \frac{1}{u - 2}$$.

Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left.\qquad 4 u^{2}-14 u+11\right) \div(u-2) \) Submit

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