Factoring Trinomials Worksheets (printable, online, answers, examples) - Free Printable

Let’s solve each trinomial by factoring.
We’re looking for two numbers that:

- Multiply to give the last number (constant term)
- Add up to give the middle number (coefficient of x)

Then we write the answer as:
(x + first number)(x + second number)

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1. $ x^2 + 18x + 80 $

Find two numbers that multiply to 80 and add to 18.

Try:
→ 8 × 10 = 80, and 8 + 10 = 18 → ✔

Answer: (x + 8)(x + 10)

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2. $ x^2 + 13x + 36 $

Multiply to 36, add to 13.

Try:
→ 4 × 9 = 36, 4 + 9 = 13 → ✔

Answer: (x + 4)(x + 9)

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3. $ x^2 + 12x + 20 $

Multiply to 20, add to 12.

Try:
→ 2 × 10 = 20, 2 + 10 = 12 → ✔

Answer: (x + 2)(x + 10)

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

Multiply to 56, add to 15.

Try:
→ 7 × 8 = 56, 7 + 8 = 15 → ✔

Answer: (x + 7)(x + 8)

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5. $ x^2 + 7x + 12 $

Multiply to 12, add to 7.

Try:
→ 3 × 4 = 12, 3 + 4 = 7 → ✔

Answer: (x + 3)(x + 4)

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6. $ x^2 + 11x + 24 $

Multiply to 24, add to 11.

Try:
→ 3 × 8 = 24, 3 + 8 = 11 → ✔

Answer: (x + 3)(x + 8)

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7. $ x^2 + 9x + 20 $

Multiply to 20, add to 9.

Try:
→ 4 × 5 = 20, 4 + 5 = 9 → ✔

Answer: (x + 4)(x + 5)

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8. $ x^2 + 16x + 64 $

Multiply to 64, add to 16.

Try:
→ 8 × 8 = 64, 8 + 8 = 16 → ✔

Answer: (x + 8)(x + 8) or (x + 8)²

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9. $ x^2 + 11x + 18 $

Multiply to 18, add to 11.

Try:
→ 2 × 9 = 18, 2 + 9 = 11 → ✔

Answer: (x + 2)(x + 9)

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

Multiply to 30, add to 11.

Try:
→ 5 × 6 = 30, 5 + 6 = 11 → ✔

Answer: (x + 5)(x + 6)

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Final Answer:
(x + 8)(x + 10)
(x + 4)(x + 9)
(x + 2)(x + 10)
(x + 7)(x + 8)
(x + 3)(x + 4)
(x + 3)(x + 8)
(x + 4)(x + 5)
(x + 8)²
(x + 2)(x + 9)
(x + 5)(x + 6)