Factoring Trinomials: a = 1 - Practice worksheet with PRODUCT and SUM grids to help factor quadratic expressions.
Worksheet for factoring trinomials with a = 1, featuring 18 quadratic expressions and PRODUCT-SUM grids for practice.
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Step-by-step solution for: Factoring Trinomials: a = 1 Worksheet | Fun and Engaging Algebra I ...
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Show Answer Key & Explanations
Step-by-step solution for: Factoring Trinomials: a = 1 Worksheet | Fun and Engaging Algebra I ...
Let’s solve each problem step by step. We’re factoring trinomials of the form x² + bx + c, where a = 1. That means we need to find two numbers that:
- Multiply to give c (the constant term) → this is the “product”
- Add to give b (the coefficient of x) → this is the “sum”
Then we write the answer as (x + first number)(x + second number).
We’ll go one by one.
---
Problem 2: x² + 9x + 8
Find two numbers that multiply to 8 and add to 9.
Factors of 8:
1 × 8 → 1 + 8 = 9 ✔
2 × 4 → 2 + 4 = 6 ✘
So, numbers are 1 and 8
Answer: (x + 1)(x + 8)
Grid:
Top box (product): 8
Bottom box (sum): 9
Left and right boxes: 1 and 8 (order doesn’t matter)
---
Problem 3: x² + 4x + 3
Multiply to 3, add to 4
Factors of 3:
1 × 3 → 1 + 3 = 4 ✔
Numbers: 1 and 3
Answer: (x + 1)(x + 3)
Grid:
Product: 3
Sum: 4
Boxes: 1 and 3
---
Problem 4: x² + 4x + 4
Multiply to 4, add to 4
Factors of 4:
1 × 4 → 1+4=5 ✘
2 × 2 → 2+2=4 ✔
Numbers: 2 and 2
Answer: (x + 2)(x + 2) or (x + 2)²
Grid:
Product: 4
Sum: 4
Boxes: 2 and 2
---
Problem 5: x² + 7x + 10
Multiply to 10, add to 7
Factors of 10:
1×10 → 11 ✘
2×5 → 2+5=7 ✔
Numbers: 2 and 5
Answer: (x + 2)(x + 5)
Grid:
Product: 10
Sum: 7
Boxes: 2 and 5
---
Problem 6: x² + 6x + 9
Multiply to 9, add to 6
Factors of 9:
1×9 → 10 ✘
3×3 → 3+3=6 ✔
Numbers: 3 and 3
Answer: (x + 3)(x + 3) or (x + 3)²
Grid:
Product: 9
Sum: 6
Boxes: 3 and 3
---
Problem 7: x² + 9x + 14
Multiply to 14, add to 9
Factors of 14:
1×14 → 15 ✘
2×7 → 2+7=9 ✔
Numbers: 2 and 7
Answer: (x + 2)(x + 7)
Grid:
Product: 14
Sum: 9
Boxes: 2 and 7
---
Problem 8: x² + 9x + 20
Multiply to 20, add to 9
Factors of 20:
1×20 → 21 ✘
2×10 → 12 ✘
4×5 → 4+5=9 ✔
Numbers: 4 and 5
Answer: (x + 4)(x + 5)
Grid:
Product: 20
Sum: 9
Boxes: 4 and 5
---
Problem 9: x² + 10x + 21
Multiply to 21, add to 10
Factors of 21:
1×21 → 22 ✘
3×7 → 3+7=10 ✔
Numbers: 3 and 7
Answer: (x + 3)(x + 7)
Grid:
Product: 21
Sum: 10
Boxes: 3 and 7
---
Problem 10: x² + 11x + 28
Multiply to 28, add to 11
Factors of 28:
1×28 → 29 ✘
2×14 → 16 ✘
4×7 → 4+7=11 ✔
Numbers: 4 and 7
Answer: (x + 4)(x + 7)
Grid:
Product: 28
Sum: 11
Boxes: 4 and 7
---
Problem 11: x² + 12x + 32
Multiply to 32, add to 12
Factors of 32:
1×32 → 33 ✘
2×16 → 18 ✘
4×8 → 4+8=12 ✔
Numbers: 4 and 8
Answer: (x + 4)(x + 8)
Grid:
Product: 32
Sum: 12
Boxes: 4 and 8
---
Problem 12: x² + 11x + 24
Multiply to 24, add to 11
Factors of 24:
1×24 → 25 ✘
2×12 → 14 ✘
3×8 → 11 ✔
4×6 → 10 ✘
Numbers: 3 and 8
Answer: (x + 3)(x + 8)
Grid:
Product: 24
Sum: 11
Boxes: 3 and 8
---
Problem 13: x² + 13x + 42
Multiply to 42, add to 13
Factors of 42:
1×42 → 43 ✘
2×21 → 23 ✘
3×14 → 17 ✘
6×7 → 6+7=13 ✔
Numbers: 6 and 7
Answer: (x + 6)(x + 7)
Grid:
Product: 42
Sum: 13
Boxes: 6 and 7
---
Problem 14: x² + 15x + 56
Multiply to 56, add to 15
Factors of 56:
1×56 → 57 ✘
2×28 → 30 ✘
4×14 → 18 ✘
7×8 → 7+8=15 ✔
Numbers: 7 and 8
Answer: (x + 7)(x + 8)
Grid:
Product: 56
Sum: 15
Boxes: 7 and 8
---
Problem 15: x² + 13x + 36
Multiply to 36, add to 13
Factors of 36:
1×36 → 37 ✘
2×18 → 20 ✘
3×12 → 15 ✘
4×9 → 13 ✔
6×6 → 12 ✘
Numbers: 4 and 9
Answer: (x + 4)(x + 9)
Grid:
Product: 36
Sum: 13
Boxes: 4 and 9
---
Problem 16: x² + 26x + 88
Multiply to 88, add to 26
Factors of 88:
1×88 → 89 ✘
2×44 → 46 ✘
4×22 → 26 ✔
8×11 → 19 ✘
Numbers: 4 and 22
Answer: (x + 4)(x + 22)
Grid:
Product: 88
Sum: 26
Boxes: 4 and 22
---
Problem 17: x² + 17x + 52
Multiply to 52, add to 17
Factors of 52:
1×52 → 53 ✘
2×26 → 28 ✘
4×13 → 4+13=17 ✔
Numbers: 4 and 13
Answer: (x + 4)(x + 13)
Grid:
Product: 52
Sum: 17
Boxes: 4 and 13
---
Problem 18: x² + 20x + 51
Multiply to 51, add to 20
Factors of 51:
1×51 → 52 ✘
3×17 → 3+17=20 ✔
Numbers: 3 and 17
Answer: (x + 3)(x + 17)
Grid:
Product: 51
Sum: 20
Boxes: 3 and 17
---
Final Answer:
2) (x + 1)(x + 8)
3) (x + 1)(x + 3)
4) (x + 2)(x + 2)
5) (x + 2)(x + 5)
6) (x + 3)(x + 3)
7) (x + 2)(x + 7)
8) (x + 4)(x + 5)
9) (x + 3)(x + 7)
10) (x + 4)(x + 7)
11) (x + 4)(x + 8)
12) (x + 3)(x + 8)
13) (x + 6)(x + 7)
14) (x + 7)(x + 8)
15) (x + 4)(x + 9)
16) (x + 4)(x + 22)
17) (x + 4)(x + 13)
18) (x + 3)(x + 17)
- Multiply to give c (the constant term) → this is the “product”
- Add to give b (the coefficient of x) → this is the “sum”
Then we write the answer as (x + first number)(x + second number).
We’ll go one by one.
---
Problem 2: x² + 9x + 8
Find two numbers that multiply to 8 and add to 9.
Factors of 8:
1 × 8 → 1 + 8 = 9 ✔
2 × 4 → 2 + 4 = 6 ✘
So, numbers are 1 and 8
Answer: (x + 1)(x + 8)
Grid:
Top box (product): 8
Bottom box (sum): 9
Left and right boxes: 1 and 8 (order doesn’t matter)
---
Problem 3: x² + 4x + 3
Multiply to 3, add to 4
Factors of 3:
1 × 3 → 1 + 3 = 4 ✔
Numbers: 1 and 3
Answer: (x + 1)(x + 3)
Grid:
Product: 3
Sum: 4
Boxes: 1 and 3
---
Problem 4: x² + 4x + 4
Multiply to 4, add to 4
Factors of 4:
1 × 4 → 1+4=5 ✘
2 × 2 → 2+2=4 ✔
Numbers: 2 and 2
Answer: (x + 2)(x + 2) or (x + 2)²
Grid:
Product: 4
Sum: 4
Boxes: 2 and 2
---
Problem 5: x² + 7x + 10
Multiply to 10, add to 7
Factors of 10:
1×10 → 11 ✘
2×5 → 2+5=7 ✔
Numbers: 2 and 5
Answer: (x + 2)(x + 5)
Grid:
Product: 10
Sum: 7
Boxes: 2 and 5
---
Problem 6: x² + 6x + 9
Multiply to 9, add to 6
Factors of 9:
1×9 → 10 ✘
3×3 → 3+3=6 ✔
Numbers: 3 and 3
Answer: (x + 3)(x + 3) or (x + 3)²
Grid:
Product: 9
Sum: 6
Boxes: 3 and 3
---
Problem 7: x² + 9x + 14
Multiply to 14, add to 9
Factors of 14:
1×14 → 15 ✘
2×7 → 2+7=9 ✔
Numbers: 2 and 7
Answer: (x + 2)(x + 7)
Grid:
Product: 14
Sum: 9
Boxes: 2 and 7
---
Problem 8: x² + 9x + 20
Multiply to 20, add to 9
Factors of 20:
1×20 → 21 ✘
2×10 → 12 ✘
4×5 → 4+5=9 ✔
Numbers: 4 and 5
Answer: (x + 4)(x + 5)
Grid:
Product: 20
Sum: 9
Boxes: 4 and 5
---
Problem 9: x² + 10x + 21
Multiply to 21, add to 10
Factors of 21:
1×21 → 22 ✘
3×7 → 3+7=10 ✔
Numbers: 3 and 7
Answer: (x + 3)(x + 7)
Grid:
Product: 21
Sum: 10
Boxes: 3 and 7
---
Problem 10: x² + 11x + 28
Multiply to 28, add to 11
Factors of 28:
1×28 → 29 ✘
2×14 → 16 ✘
4×7 → 4+7=11 ✔
Numbers: 4 and 7
Answer: (x + 4)(x + 7)
Grid:
Product: 28
Sum: 11
Boxes: 4 and 7
---
Problem 11: x² + 12x + 32
Multiply to 32, add to 12
Factors of 32:
1×32 → 33 ✘
2×16 → 18 ✘
4×8 → 4+8=12 ✔
Numbers: 4 and 8
Answer: (x + 4)(x + 8)
Grid:
Product: 32
Sum: 12
Boxes: 4 and 8
---
Problem 12: x² + 11x + 24
Multiply to 24, add to 11
Factors of 24:
1×24 → 25 ✘
2×12 → 14 ✘
3×8 → 11 ✔
4×6 → 10 ✘
Numbers: 3 and 8
Answer: (x + 3)(x + 8)
Grid:
Product: 24
Sum: 11
Boxes: 3 and 8
---
Problem 13: x² + 13x + 42
Multiply to 42, add to 13
Factors of 42:
1×42 → 43 ✘
2×21 → 23 ✘
3×14 → 17 ✘
6×7 → 6+7=13 ✔
Numbers: 6 and 7
Answer: (x + 6)(x + 7)
Grid:
Product: 42
Sum: 13
Boxes: 6 and 7
---
Problem 14: x² + 15x + 56
Multiply to 56, add to 15
Factors of 56:
1×56 → 57 ✘
2×28 → 30 ✘
4×14 → 18 ✘
7×8 → 7+8=15 ✔
Numbers: 7 and 8
Answer: (x + 7)(x + 8)
Grid:
Product: 56
Sum: 15
Boxes: 7 and 8
---
Problem 15: x² + 13x + 36
Multiply to 36, add to 13
Factors of 36:
1×36 → 37 ✘
2×18 → 20 ✘
3×12 → 15 ✘
4×9 → 13 ✔
6×6 → 12 ✘
Numbers: 4 and 9
Answer: (x + 4)(x + 9)
Grid:
Product: 36
Sum: 13
Boxes: 4 and 9
---
Problem 16: x² + 26x + 88
Multiply to 88, add to 26
Factors of 88:
1×88 → 89 ✘
2×44 → 46 ✘
4×22 → 26 ✔
8×11 → 19 ✘
Numbers: 4 and 22
Answer: (x + 4)(x + 22)
Grid:
Product: 88
Sum: 26
Boxes: 4 and 22
---
Problem 17: x² + 17x + 52
Multiply to 52, add to 17
Factors of 52:
1×52 → 53 ✘
2×26 → 28 ✘
4×13 → 4+13=17 ✔
Numbers: 4 and 13
Answer: (x + 4)(x + 13)
Grid:
Product: 52
Sum: 17
Boxes: 4 and 13
---
Problem 18: x² + 20x + 51
Multiply to 51, add to 20
Factors of 51:
1×51 → 52 ✘
3×17 → 3+17=20 ✔
Numbers: 3 and 17
Answer: (x + 3)(x + 17)
Grid:
Product: 51
Sum: 20
Boxes: 3 and 17
---
Final Answer:
2) (x + 1)(x + 8)
3) (x + 1)(x + 3)
4) (x + 2)(x + 2)
5) (x + 2)(x + 5)
6) (x + 3)(x + 3)
7) (x + 2)(x + 7)
8) (x + 4)(x + 5)
9) (x + 3)(x + 7)
10) (x + 4)(x + 7)
11) (x + 4)(x + 8)
12) (x + 3)(x + 8)
13) (x + 6)(x + 7)
14) (x + 7)(x + 8)
15) (x + 4)(x + 9)
16) (x + 4)(x + 22)
17) (x + 4)(x + 13)
18) (x + 3)(x + 17)
Parent Tip: Review the logic above to help your child master the concept of factoring quadratics worksheet a 1.
