Factoring perfect trinomial worksheet - Free Printable

Absolutely! Let’s solve this worksheet step by step. The topic is Factoring Perfect Square Trinomials.

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## 🔷 Part A: Complete the expression to make a perfect square trinomial

A perfect square trinomial has the form:

> (x + b)² = x² + 2bx + b²
> or
> (x - b)² = x² - 2bx + b²

So, given an expression like `a² + 8a + ___`, we need to find the constant term that makes it a perfect square.

✔ Strategy:

Take the coefficient of the middle term (the “a” term), divide it by 2, then square it.

That is:
> Constant = (middle coefficient ÷ 2)²

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Let’s solve each one:

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1) a² + 8a + ___

- Middle coefficient = 8
- 8 ÷ 2 = 4 → 4² = 16
✔ Answer: 16

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2) a² – 10a + ___

- Middle coefficient = -10 → take absolute value for squaring: 10
- 10 ÷ 2 = 5 → 5² = 25
✔ Answer: 25

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3) a² + 4a + ___

- 4 ÷ 2 = 2 → 2² = 4
✔ Answer: 4

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4) a² – 24a + ___

- 24 ÷ 2 = 12 → 12² = 144
✔ Answer: 144

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5) a² – 4a + ___

- 4 ÷ 2 = 2 → 2² = 4
✔ Answer: 4

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6) a² + 24a + ___

- 24 ÷ 2 = 12 → 12² = 144
✔ Answer: 144

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7) a² + 12a + ___

- 12 ÷ 2 = 6 → 6² = 36
✔ Answer: 36

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8) a² – 12a + ___

- 12 ÷ 2 = 6 → 6² = 36
✔ Answer: 36

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9) a² – 6a + ___

- 6 ÷ 2 = 3 → 3² = 9
✔ Answer: 9

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10) a² + 10a + ___

- 10 ÷ 2 = 5 → 5² = 25
✔ Answer: 25

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## 🟩 Part A Answers Summary:

1) 16
2) 25
3) 4
4) 144
5) 4
6) 144
7) 36
8) 36
9) 9
10) 25

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## 🔷 Part B: Match Column A with its factor in Column B

We’ll use the same perfect square formulas:

> (x + b)² = x² + 2bx + b²
> (x - b)² = x² - 2bx + b²

We’ll match each trinomial in Column A to its factored form in Column B.

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1. a² + 8a + 16

- Compare to (a + 4)² = a² + 8a + 16 → ✔ Matches (a + 4)²

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2. a² – 10a + 25

- (a – 5)² = a² – 10a + 25 → ✔ Matches (a – 5)²

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3. 4a² – 4a + 1

- This is (2a – 1)² = 4a² – 4a + 1 → ✔ Matches (2a – 1)²

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4. 4a² – 12a + 9

- (2a – 3)² = 4a² – 12a + 9 → ✔ Matches (2a – 3)²

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5. 4a² + 4a + 1

- (2a + 1)² = 4a² + 4a + 1 → ✔ Matches (2a + 1)²

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6. 9a² + 24a + 16

- (3a + 4)² = 9a² + 24a + 16 → ✔ Matches (3a + 4)²

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7. a² + 12a + 36

- (a + 6)² = a² + 12a + 36 → ✔ Matches (a + 6)²

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8. a² – 12a + 36

- (a – 6)² = a² – 12a + 36 → ✔ Matches (a – 6)²

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9. a² – 8a + 16

- (a – 4)² = a² – 8a + 16 → ✔ Matches (a – 4)²

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10. a² + 10a + 25

- (a + 5)² = a² + 10a + 25 → ✔ Matches (a + 5)²

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## 🟩 Part B Matching Summary:

| Column A | Matches With |
|---------------------------|--------------------|
| 1. a² + 8a + 16 | (a + 4)² |
| 2. a² – 10a + 25 | (a – 5)² |
| 3. 4a² – 4a + 1 | (2a – 1)² |
| 4. 4a² – 12a + 9 | (2a – 3)² |
| 5. 4a² + 4a + 1 | (2a + 1)² |
| 6. 9a² + 24a + 16 | (3a + 4)² |
| 7. a² + 12a + 36 | (a + 6)² |
| 8. a² – 12a + 36 | (a – 6)² |
| 9. a² – 8a + 16 | (a – 4)² |
| 10. a² + 10a + 25 | (a + 5)² |

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## ✔ Final Answers:

Part A:

1) 16
2) 25
3) 4
4) 144
5) 4
6) 144
7) 36
8) 36
9) 9
10) 25

Part B:

Match as above — draw lines from:

- 1 → (a + 4)²
- 2 → (a – 5)²
- 3 → (2a – 1)²
- 4 → (2a – 3)²
- 5 → (2a + 1)²
- 6 → (3a + 4)²
- 7 → (a + 6)²
- 8 → (a – 6)²
- 9 → (a – 4)²
- 10 → (a + 5)²

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✔ You’ve now mastered completing and factoring perfect square trinomials!

Let me know if you’d like a printable version or more practice problems! 😊