You've uploaded a worksheet titled
“Factoring Trinomials”, which asks you to factor 10 quadratic trinomials of the form:
>
x² + bx + c
These are called
monic trinomials (leading coefficient = 1). To factor them, we need to find two numbers that:
- Multiply to give
c (the constant term)
- Add to give
b (the coefficient of the middle term)
Then, we write the factored form as:
>
(x + m)(x + n)
where
m × n = c and
m + n = b
---
Let’s solve each one step by step.
---
1. x² + 18x + 80
Find two numbers that multiply to
80 and add to
18.
Factors of 80:
- 1×80 → 1+80=81
✘
- 2×40 → 2+40=42
✘
- 4×20 → 4+20=24
✘
-
8×10 → 8+10=18 ✔
✔ So, factors are
(x + 8)(x + 10)
---
2. x² + 13x + 36
Find two numbers that multiply to
36 and add to
13.
Factors of 36:
- 1×36 → 37
✘
- 2×18 → 20
✘
- 3×12 → 15
✘
-
4×9 → 13 ✔
✔ So, factors are
(x + 4)(x + 9)
---
3. x² + 12x + 20
Multiply to 20, add to 12.
Factors:
- 1×20 → 21
✘
-
2×10 → 12 ✔
✔ So, factors are
(x + 2)(x + 10)
---
4. x² + 15x + 56
Multiply to 56, add to 15.
Factors:
- 1×56 → 57
✘
- 2×28 → 30
✘
- 4×14 → 18
✘
-
7×8 → 15 ✔
✔ So, factors are
(x + 7)(x + 8)
---
5. x² + 7x + 12
Multiply to 12, add to 7.
Factors:
- 1×12 → 13
✘
-
3×4 → 7 ✔
✔ So, factors are
(x + 3)(x + 4)
---
6. x² + 11x + 24
Multiply to 24, add to 11.
Factors:
- 1×24 → 25
✘
- 2×12 → 14
✘
-
3×8 → 11 ✔
✔ So, factors are
(x + 3)(x + 8)
---
7. x² + 9x + 20
Multiply to 20, add to 9.
Factors:
- 1×20 → 21
✘
-
4×5 → 9 ✔
✔ So, factors are
(x + 4)(x + 5)
---
8. x² + 16x + 64
Multiply to 64, add to 16.
Factors:
- 1×64 → 65
✘
- 2×32 → 34
✘
- 4×16 → 20
✘
-
8×8 → 16 ✔
✔ So, factors are
(x + 8)(x + 8) = (x + 8)²
---
9. x² + 11x + 18
Multiply to 18, add to 11.
Factors:
- 1×18 → 19
✘
-
2×9 → 11 ✔
✔ So, factors are
(x + 2)(x + 9)
---
10. x² + 11x + 30
Multiply to 30, add to 11.
Factors:
- 1×30 → 31
✘
- 2×15 → 17
✘
-
5×6 → 11 ✔
✔ So, factors are
(x + 5)(x + 6)
---
##
✔ Final Answers:
1.
x² + 18x + 80 →
(x + 8)(x + 10)
2.
x² + 13x + 36 →
(x + 4)(x + 9)
3.
x² + 12x + 20 →
(x + 2)(x + 10)
4.
x² + 15x + 56 →
(x + 7)(x + 8)
5.
x² + 7x + 12 →
(x + 3)(x + 4)
6.
x² + 11x + 24 →
(x + 3)(x + 8)
7.
x² + 9x + 20 →
(x + 4)(x + 5)
8.
x² + 16x + 64 →
(x + 8)²
9.
x² + 11x + 18 →
(x + 2)(x + 9)
10.
x² + 11x + 30 →
(x + 5)(x + 6)
---
## 💡 Tip for Factoring:
Always start with the
factors closest to the square root of the constant term — they’re more likely to add up to the middle coefficient. Also, remember to check signs! Since all constants here are positive and the middle terms are positive, both factors will be
positive.
Let me know if you’d like to see how to factor trinomials where the leading coefficient is *not* 1!
Parent Tip: Review the logic above to help your child master the concept of factoring trinomials worksheet answers.
