Factoring Trinomials: a = 1 Worksheet | Fun and Engaging Algebra I ... - Free Printable

Let’s solve each problem step by step. We’re factoring trinomials of the form x² + bx + c, where we need to find two numbers that:

- Multiply to give c (the constant term) → this goes in the top box (“product”)
- Add to give b (the coefficient of x) → this goes in the bottom box (“sum”)

Then, we write the factors as (x + first number)(x + second number).

We’ll go one by one.

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Problem 1)
Already done: x² + 5x + 6 → numbers are 3 and 2 → (x+3)(x+2) ✔

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Problem 2)
x² + 9x + 8
Need two numbers that multiply to 8 and add to 9.
→ 8 and 1 → 8×1=8, 8+1=9
So: (x + 8)(x + 1)

Grid:
Top: 8
Middle left/right: 8 and 1
Bottom: 9

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Problem 3)
x² + 4x + 3
Multiply to 3, add to 4 → 3 and 1
→ (x + 3)(x + 1)

Grid:
Top: 3
Middle: 3 and 1
Bottom: 4

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Problem 4)
x² + 4x + 4
Multiply to 4, add to 4 → 2 and 2
→ (x + 2)(x + 2) or (x + 2)²

Grid:
Top: 4
Middle: 2 and 2
Bottom: 4

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Problem 5)
x² + 7x + 10
Multiply to 10, add to 7 → 5 and 2
→ (x + 5)(x + 2)

Grid:
Top: 10
Middle: 5 and 2
Bottom: 7

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Problem 6)
x² + 6x + 9
Multiply to 9, add to 6 → 3 and 3
→ (x + 3)(x + 3) or (x + 3)²

Grid:
Top: 9
Middle: 3 and 3
Bottom: 6

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Problem 7)
x² + 9x + 14
Multiply to 14, add to 9 → 7 and 2
→ (x + 7)(x + 2)

Grid:
Top: 14
Middle: 7 and 2
Bottom: 9

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Problem 8)
x² + 9x + 20
Multiply to 20, add to 9 → 5 and 4
→ (x + 5)(x + 4)

Grid:
Top: 20
Middle: 5 and 4
Bottom: 9

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Problem 9)
x² + 10x + 21
Multiply to 21, add to 10 → 7 and 3
→ (x + 7)(x + 3)

Grid:
Top: 21
Middle: 7 and 3
Bottom: 10

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Problem 10)
x² + 11x + 28
Multiply to 28, add to 11 → 7 and 4
→ (x + 7)(x + 4)

Grid:
Top: 28
Middle: 7 and 4
Bottom: 11

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Problem 11)
x² + 12x + 32
Multiply to 32, add to 12 → 8 and 4
→ (x + 8)(x + 4)

Grid:
Top: 32
Middle: 8 and 4
Bottom: 12

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Problem 12)
x² + 11x + 24
Multiply to 24, add to 11 → 8 and 3
→ (x + 8)(x + 3)

Grid:
Top: 24
Middle: 8 and 3
Bottom: 11

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Problem 13)
x² + 13x + 42
Multiply to 42, add to 13 → 7 and 6
→ (x + 7)(x + 6)

Grid:
Top: 42
Middle: 7 and 6
Bottom: 13

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Problem 14)
x² + 15x + 56
Multiply to 56, add to 15 → 8 and 7
→ (x + 8)(x + 7)

Grid:
Top: 56
Middle: 8 and 7
Bottom: 15

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Problem 15)
x² + 13x + 36
Multiply to 36, add to 13 → 9 and 4
→ (x + 9)(x + 4)

Grid:
Top: 36
Middle: 9 and 4
Bottom: 13

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Problem 16)
x² + 26x + 88
Multiply to 88, add to 26 → Let’s list factor pairs of 88:
1 & 88 → sum 89
2 & 44 → 46
4 & 22 → 26 ← YES!
→ (x + 4)(x + 22)

Grid:
Top: 88
Middle: 4 and 22
Bottom: 26

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Problem 17)
x² + 17x + 52
Factor pairs of 52:
1 & 52 → 53
2 & 26 → 28
4 & 13 → 17 ← YES!
→ (x + 4)(x + 13)

Grid:
Top: 52
Middle: 4 and 13
Bottom: 17

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Problem 18)
x² + 20x + 51
Factor pairs of 51:
1 & 51 → 52
3 & 17 → 20 ← YES!
→ (x + 3)(x + 17)

Grid:
Top: 51
Middle: 3 and 17
Bottom: 20

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All problems solved carefully with verified multiplication and addition.

Final Answer:
2) (x + 8)(x + 1)
3) (x + 3)(x + 1)
4) (x + 2)(x + 2)
5) (x + 5)(x + 2)
6) (x + 3)(x + 3)
7) (x + 7)(x + 2)
8) (x + 5)(x + 4)
9) (x + 7)(x + 3)
10) (x + 7)(x + 4)
11) (x + 8)(x + 4)
12) (x + 8)(x + 3)
13) (x + 7)(x + 6)
14) (x + 8)(x + 7)
15) (x + 9)(x + 4)
16) (x + 4)(x + 22)
17) (x + 4)(x + 13)
18) (x + 3)(x + 17)