Factoring Trinomials Practice Worksheet

It looks like you've uploaded a worksheet titled "Factoring Trinomials" with a series of algebra problems. However, the image isn't visible to me, so I can't directly see the specific problems or their content.

But based on your description and the typical format of such worksheets, here’s how we can proceed:

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🔍 What is the task?

The goal is to factor each trinomial completely, if possible. If it cannot be factored, write "prime."

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📌 General Strategy for Factoring Trinomials

For a trinomial in the form:
$$
ax^2 + bx + c
$$

We look for two numbers that:
- Multiply to $ a \cdot c $
- Add to $ b $

Then use those numbers to split the middle term and factor by grouping.

For example:
> Factor: $ x^2 + 5x + 6 $

- Find two numbers that multiply to $ 6 $ (since $ a = 1 $, $ c = 6 $) and add to $ 5 $
- Numbers: $ 2 $ and $ 3 $
- So: $ x^2 + 5x + 6 = (x + 2)(x + 3) $

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Since I can’t see the actual problems, let me assume some common types from the list and show how to solve them.

Let’s suppose the problems are similar to these:

1. $ x^2 + 7x + 12 $
2. $ x^2 - 9x + 20 $
3. $ x^2 + 4x - 12 $
4. $ 2x^2 + 7x + 3 $
5. $ x^2 - 8x + 16 $

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✔ Example Solutions

#### 1. $ x^2 + 7x + 12 $
- Need two numbers that multiply to 12 and add to 7 → $ 3 $ and $ 4 $
- $ (x + 3)(x + 4) $

#### 2. $ x^2 - 9x + 20 $
- Multiply to 20, add to -9 → $ -4 $ and $ -5 $
- $ (x - 4)(x - 5) $

#### 3. $ x^2 + 4x - 12 $
- Multiply to -12, add to 4 → $ 6 $ and $ -2 $
- $ (x + 6)(x - 2) $

#### 4. $ 2x^2 + 7x + 3 $
- Use AC method: $ a = 2 $, $ c = 3 $, $ ac = 6 $
- Find factors of 6 that add to 7 → $ 6 $ and $ 1 $
- Split middle term: $ 2x^2 + 6x + x + 3 $
- Group: $ (2x^2 + 6x) + (x + 3) = 2x(x + 3) + 1(x + 3) $
- Factor: $ (2x + 1)(x + 3) $

#### 5. $ x^2 - 8x + 16 $
- Perfect square trinomial: $ (x - 4)^2 $

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✘ When to Write "Prime"

If no such pair of numbers exists, write "prime".

Example:
$ x^2 + x + 1 $ → No integers multiply to 1 and add to 1 → prime

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💡 Tips

- Always check for GCF first.
- For trinomials with $ a \neq 1 $, use AC method or trial and error.
- Look for perfect squares or difference of squares.

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📝 Final Advice

Since I can't view your image, please describe the problems or type them out, and I’ll help you factor each one step-by-step!

Or, if you can paste the exact expressions from the worksheet, I’ll solve them all for you.

Just reply with the list of problems!