To divide \((x^2 + 3x + 2)\) by \((x + 2)\), we can use polynomial division.

### Step 1: Set up the division

We are dividing \(x^2 + 3x + 2\) by \(x + 2\).

\[
\text{Divide } x^2 \text{ by } x, \text{ which gives } x.
\]

### Step 2: Multiply and subtract

Now, multiply \(x\) by \(x + 2\), which gives \(x^2 + 2x\). Subtract this from the original polynomial:

\[
(x^2 + 3x + 2) - (x^2 + 2x) = x + 2
\]

### Step 3: Divide again

Next, divide \(x\) by \(x\), which gives \(1\).

### Step 4: Multiply and subtract

Multiply \(1\) by \(x + 2\), which gives \(x + 2\). Subtract:

\[
(x + 2) - (x + 2) = 0
\]

There is no remainder.

### Final Answer:
The quotient is \(x + 1\).

Would you like more details on polynomial division or have any other questions?

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Here are 5 related questions for practice:
1. Divide \(x^3 + 5x^2 + 6x + 4\) by \(x + 2\).
2. Perform synthetic division for \((x^2 - x - 12)\) divided by \((x - 3)\).
3. Divide \(2x^2 + 7x + 3\) by \(x + 1\).
4. How do you factor \(x^2 + 3x + 2\) completely?
5. Perform long division for \((3x^3 + 2x^2 + x)\) divided by \((x + 1)\).

**Tip:** When dividing polynomials, always align terms with the same degree to avoid mistakes.

Learn how to divide the polynomial x^2 + 3x + 2 by x + 2 using polynomial division. Detailed step-by-step solution provided. Suitable for high school students studying polynomial division.

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