Grade 9 Factoring Trinomials Worksheets 2024 - Free Printable

Let's solve each trinomial factoring problem step by step. We'll factor each quadratic expression completely, starting by checking for a Greatest Common Factor (GCF) if applicable.

---

General Strategy:

For a trinomial in the form $ x^2 + bx + c $, we look for two numbers that:
- Multiply to $ c $
- Add to $ b $

For trinomials with a leading coefficient other than 1 (like $ ax^2 + bx + c $), we use factoring by grouping or AC method.

---

Now let’s go through each one:

---

1. $ x^2 + 13x - 30 $

We need two numbers that multiply to $-30$ and add to $13$.
Try: $15$ and $-2$: $15 \times (-2) = -30$, $15 + (-2) = 13$ ✔

$$
= (x + 15)(x - 2)
$$

✔ Answer: $ (x + 15)(x - 2) $

---

2. $ x^2 - 5x - 24 $

Need two numbers that multiply to $-24$ and add to $-5$.
Try: $-8$ and $3$: $-8 \times 3 = -24$, $-8 + 3 = -5$ ✔

$$
= (x - 8)(x + 3)
$$

✔ Answer: $ (x - 8)(x + 3) $

---

3. $ x^2 + 5x - 36 $

Need two numbers that multiply to $-36$ and add to $5$.
Try: $9$ and $-4$: $9 \times (-4) = -36$, $9 + (-4) = 5$ ✔

$$
= (x + 9)(x - 4)
$$

✔ Answer: $ (x + 9)(x - 4) $

---

4. $ x^2 + 15x + 56 $

Need two numbers that multiply to $56$ and add to $15$.
Try: $7$ and $8$: $7 \times 8 = 56$, $7 + 8 = 15$ ✔

$$
= (x + 7)(x + 8)
$$

✔ Answer: $ (x + 7)(x + 8) $

---

5. $ x^2 + 15x + 54 $

Need two numbers that multiply to $54$ and add to $15$.
Try: $6$ and $9$: $6 \times 9 = 54$, $6 + 9 = 15$ ✔

$$
= (x + 6)(x + 9)
$$

✔ Answer: $ (x + 6)(x + 9) $

---

6. $ x^2 - 8x - 20 $

Need two numbers that multiply to $-20$ and add to $-8$.
Try: $-10$ and $2$: $-10 \times 2 = -20$, $-10 + 2 = -8$ ✔

$$
= (x - 10)(x + 2)
$$

✔ Answer: $ (x - 10)(x + 2) $

---

7. $ x^2 + 4x - 32 $

Need two numbers that multiply to $-32$ and add to $4$.
Try: $8$ and $-4$: $8 \times (-4) = -32$, $8 + (-4) = 4$ ✔

$$
= (x + 8)(x - 4)
$$

✔ Answer: $ (x + 8)(x - 4) $

---

8. $ x^2 - x - 20 $

Need two numbers that multiply to $-20$ and add to $-1$.
Try: $-5$ and $4$: $-5 \times 4 = -20$, $-5 + 4 = -1$ ✔

$$
= (x - 5)(x + 4)
$$

✔ Answer: $ (x - 5)(x + 4) $

---

9. $ x^2 + 11x + 30 $

Need two numbers that multiply to $30$ and add to $11$.
Try: $5$ and $6$: $5 \times 6 = 30$, $5 + 6 = 11$ ✔

$$
= (x + 5)(x + 6)
$$

✔ Answer: $ (x + 5)(x + 6) $

---

10. $ x^2 + 14x + 49 $

This is a perfect square trinomial.
Check: $14/2 = 7$, $7^2 = 49$

$$
= (x + 7)^2
$$

✔ Answer: $ (x + 7)^2 $

---

11. $ x^2 + 10x + 16 $

Need two numbers that multiply to $16$ and add to $10$.
Try: $8$ and $2$: $8 \times 2 = 16$, $8 + 2 = 10$ ✔

$$
= (x + 8)(x + 2)
$$

✔ Answer: $ (x + 8)(x + 2) $

---

12. $ x^2 + 3x + 2 $

Need two numbers that multiply to $2$ and add to $3$.
Try: $1$ and $2$: $1 \times 2 = 2$, $1 + 2 = 3$ ✔

$$
= (x + 1)(x + 2)
$$

✔ Answer: $ (x + 1)(x + 2) $

---

13. $ x^2 + 15x + 44 $

Need two numbers that multiply to $44$ and add to $15$.
Try: $11$ and $4$: $11 \times 4 = 44$, $11 + 4 = 15$ ✔

$$
= (x + 11)(x + 4)
$$

✔ Answer: $ (x + 11)(x + 4) $

---

14. Missing on sheet — skip

---

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

Need two numbers that multiply to $5$ and add to $6$.
Try: $5$ and $1$: $5 \times 1 = 5$, $5 + 1 = 6$ ✔

$$
= (x + 5)(x + 1)
$$

✔ Answer: $ (x + 5)(x + 1) $

---

16. $ 2x^2 + 20x + 32 $

First, check GCF: All terms divisible by 2.

Factor out GCF:
$$
= 2(x^2 + 10x + 16)
$$

Now factor $ x^2 + 10x + 16 $: need two numbers that multiply to $16$ and add to $10$: $8$ and $2$

$$
= 2(x + 8)(x + 2)
$$

✔ Answer: $ 2(x + 8)(x + 2) $

---

17. Missing on sheet — skip

---

18. $ 3x^2 - 15x + 18 $

Check GCF: all terms divisible by 3.

Factor out GCF:
$$
= 3(x^2 - 5x + 6)
$$

Now factor $ x^2 - 5x + 6 $: need two numbers that multiply to $6$ and add to $-5$: $-3$ and $-2$

$$
= 3(x - 3)(x - 2)
$$

✔ Answer: $ 3(x - 3)(x - 2) $

---

19. $ 2x^2 + 8x - 24 $

Check GCF: all terms divisible by 2.

Factor out GCF:
$$
= 2(x^2 + 4x - 12)
$$

Now factor $ x^2 + 4x - 12 $: need two numbers that multiply to $-12$ and add to $4$: $6$ and $-2$

$$
= 2(x + 6)(x - 2)
$$

✔ Answer: $ 2(x + 6)(x - 2) $

---

20. $ 2x^2 + 16x - 32 $

Check GCF: all terms divisible by 2.

Factor out GCF:
$$
= 2(x^2 + 8x - 16)
$$

Now factor $ x^2 + 8x - 16 $. Try to find two numbers that multiply to $-16$ and add to $8$.
Possible pairs:
- $8$ and $-2$: $8 \times (-2) = -16$, $8 + (-2) = 6$ ✘
- $16$ and $-1$: $16 + (-1) = 15$ ✘
- $4$ and $-4$: sum = 0 ✘
No integer pair works → does not factor over integers.

So, this trinomial cannot be factored further using integers.

✔ Answer: $ 2(x^2 + 8x - 16) $ ← Not factorable over integers

---

✔ Final Answers Summary:

| Problem | Factored Form |
|--------|----------------|
| 1 | $ (x + 15)(x - 2) $ |
| 2 | $ (x - 8)(x + 3) $ |
| 3 | $ (x + 9)(x - 4) $ |
| 4 | $ (x + 7)(x + 8) $ |
| 5 | $ (x + 6)(x + 9) $ |
| 6 | $ (x - 10)(x + 2) $ |
| 7 | $ (x + 8)(x - 4) $ |
| 8 | $ (x - 5)(x + 4) $ |
| 9 | $ (x + 5)(x + 6) $ |
| 10 | $ (x + 7)^2 $ |
| 11 | $ (x + 8)(x + 2) $ |
| 12 | $ (x + 1)(x + 2) $ |
| 13 | $ (x + 11)(x + 4) $ |
| 15 | $ (x + 5)(x + 1) $ |
| 16 | $ 2(x + 8)(x + 2) $ |
| 18 | $ 3(x - 3)(x - 2) $ |
| 19 | $ 2(x + 6)(x - 2) $ |
| 20 | $ 2(x^2 + 8x - 16) $ → Not factorable over integers |

> 🔍 Note: Problems 14 and 17 are missing from the worksheet.

Let me know if you'd like help solving any of them using the quadratic formula or completing the square!