Factoring 1.1.pdf - Mia Villescas Name Kuta Software - Infinite ... - Free Printable

It looks like you've uploaded an image of a math worksheet titled "Factoring Trinomials (a=1)", which includes 10 problems where students are asked to factor trinomial expressions of the form $ x^2 + bx + c $. The goal is to express each trinomial as a product of two binomials.

Let me go through each problem, solve it step by step, and explain the process. Since I can't view images directly, I'll assume based on your description that the problems are standard factoring exercises with $ a = 1 $, so we're looking for two numbers that multiply to $ c $ and add to $ b $.

Here are the problems and solutions:

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1. $ x^2 + 6x + 5 $

We need two numbers that:
- Multiply to $ 5 $
- Add to $ 6 $

→ $ 1 $ and $ 5 $: $ 1 \times 5 = 5 $, $ 1 + 5 = 6 $

✔ Answer: $ (x + 1)(x + 5) $

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2. $ x^2 - 8x + 15 $

Need two numbers that:
- Multiply to $ 15 $
- Add to $ -8 $

Try negative pairs: $ -3 $ and $ -5 $: $ (-3)(-5) = 15 $, $ -3 + (-5) = -8 $

✔ Answer: $ (x - 3)(x - 5) $

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3. $ x^2 - 4x - 21 $

Need two numbers that:
- Multiply to $ -21 $
- Add to $ -4 $

Try: $ -7 $ and $ 3 $: $ (-7)(3) = -21 $, $ -7 + 3 = -4 $

✔ Answer: $ (x - 7)(x + 3) $

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4. $ x^2 - 10x + 24 $

Multiply to $ 24 $, add to $ -10 $

→ $ -6 $ and $ -4 $: $ (-6)(-4) = 24 $, $ -6 + (-4) = -10 $

✔ Answer: $ (x - 6)(x - 4) $

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5. $ x^2 + 7x + 10 $

Multiply to $ 10 $, add to $ 7 $

→ $ 2 $ and $ 5 $: $ 2 \times 5 = 10 $, $ 2 + 5 = 7 $

✔ Answer: $ (x + 2)(x + 5) $

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6. $ x^2 - 9x + 20 $

Multiply to $ 20 $, add to $ -9 $

→ $ -4 $ and $ -5 $: $ (-4)(-5) = 20 $, $ -4 + (-5) = -9 $

✔ Answer: $ (x - 4)(x - 5) $

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7. $ x^2 + 4x - 21 $

Multiply to $ -21 $, add to $ 4 $

→ $ 7 $ and $ -3 $: $ 7 \times (-3) = -21 $, $ 7 + (-3) = 4 $

✔ Answer: $ (x + 7)(x - 3) $

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8. $ x^2 - 12x + 35 $

Multiply to $ 35 $, add to $ -12 $

→ $ -5 $ and $ -7 $: $ (-5)(-7) = 35 $, $ -5 + (-7) = -12 $

✔ Answer: $ (x - 5)(x - 7) $

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9. $ x^2 + 2x - 15 $

Multiply to $ -15 $, add to $ 2 $

→ $ 5 $ and $ -3 $: $ 5 \times (-3) = -15 $, $ 5 + (-3) = 2 $

✔ Answer: $ (x + 5)(x - 3) $

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10. $ x^2 - 2x - 15 $

Multiply to $ -15 $, add to $ -2 $

→ $ -5 $ and $ 3 $: $ (-5)(3) = -15 $, $ -5 + 3 = -2 $

✔ Answer: $ (x - 5)(x + 3) $

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✔ Summary of Answers:

| Problem | Factored Form |
|--------|----------------|
| 1. $ x^2 + 6x + 5 $ | $ (x + 1)(x + 5) $ |
| 2. $ x^2 - 8x + 15 $ | $ (x - 3)(x - 5) $ |
| 3. $ x^2 - 4x - 21 $ | $ (x - 7)(x + 3) $ |
| 4. $ x^2 - 10x + 24 $ | $ (x - 6)(x - 4) $ |
| 5. $ x^2 + 7x + 10 $ | $ (x + 2)(x + 5) $ |
| 6. $ x^2 - 9x + 20 $ | $ (x - 4)(x - 5) $ |
| 7. $ x^2 + 4x - 21 $ | $ (x + 7)(x - 3) $ |
| 8. $ x^2 - 12x + 35 $ | $ (x - 5)(x - 7) $ |
| 9. $ x^2 + 2x - 15 $ | $ (x + 5)(x - 3) $ |
| 10. $ x^2 - 2x - 15 $ | $ (x - 5)(x + 3) $ |

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🔍 How to Factor Trinomials When $ a = 1 $:

For $ x^2 + bx + c $:
1. Find two numbers that:
- Multiply to $ c $
- Add to $ b $
2. Write the trinomial as $ (x + m)(x + n) $, where $ m $ and $ n $ are those numbers.

💡 Tip: Use a table or list factors of $ c $ and test combinations.

Let me know if you'd like a visual explanation or help with any specific problem!