Factoring Quadratic Equations Worksheets - Free Printable

I'll solve these quadratic equations by factoring them. Let me work through each one carefully.

Problem 2: a² + 7a + 6 = 0
- Need two numbers that multiply to 6 and add to 7
- 6 × 1 = 6 and 6 + 1 = 7 ✓
- Factors: (a + 6)(a + 1) = 0
- Solutions: a = -6 or a = -1

Problem 3: b² + 4b + 4 = 0
- Need two numbers that multiply to 4 and add to 4
- 2 × 2 = 4 and 2 + 2 = 4 ✓
- Factors: (b + 2)(b + 2) = 0 or (b + 2)² = 0
- Solution: b = -2

Problem 4: c² + 5c + 6 = 0
- Need two numbers that multiply to 6 and add to 5
- 3 × 2 = 6 and 3 + 2 = 5 ✓
- Factors: (c + 3)(c + 2) = 0
- Solutions: c = -3 or c = -2

Problem 5: d² + 8d + 12 = 0
- Need two numbers that multiply to 12 and add to 8
- 6 × 2 = 12 and 6 + 2 = 8 ✓
- Factors: (d + 6)(d + 2) = 0
- Solutions: d = -6 or d = -2

Problem 6: e² + 6e + 8 = 0
- Need two numbers that multiply to 8 and add to 6
- 4 × 2 = 8 and 4 + 2 = 6 ✓
- Factors: (e + 4)(e + 2) = 0
- Solutions: e = -4 or e = -2

Problem 7: f² + 7f + 10 = 0
- Need two numbers that multiply to 10 and add to 7
- 5 × 2 = 10 and 5 + 2 = 7 ✓
- Factors: (f + 5)(f + 2) = 0
- Solutions: f = -5 or f = -2

Problem 8: g² + 8g + 7 = 0
- Need two numbers that multiply to 7 and add to 8
- 7 × 1 = 7 and 7 + 1 = 8 ✓
- Factors: (g + 7)(g + 1) = 0
- Solutions: g = -7 or g = -1

Problem 9: h² + 10h + 9 = 0
- Need two numbers that multiply to 9 and add to 10
- 9 × 1 = 9 and 9 + 1 = 10 ✓
- Factors: (h + 9)(h + 1) = 0
- Solutions: h = -9 or h = -1

Problem 10: i² + 8i + 16 = 0
- Need two numbers that multiply to 16 and add to 8
- 4 × 4 = 16 and 4 + 4 = 8 ✓
- Factors: (i + 4)(i + 4) = 0 or (i + 4)² = 0
- Solution: i = -4

Problem 11: j² + 7j + 12 = 0
- Need two numbers that multiply to 12 and add to 7
- 4 × 3 = 12 and 4 + 3 = 7 ✓
- Factors: (j + 4)(j + 3) = 0
- Solutions: j = -4 or j = -3

Problem 12: k² + 10k + 16 = 0
- Need two numbers that multiply to 16 and add to 10
- 8 × 2 = 16 and 8 + 2 = 10 ✓
- Factors: (k + 8)(k + 2) = 0
- Solutions: k = -8 or k = -2

Problem 13: m² + 8m + 15 = 0
- Need two numbers that multiply to 15 and add to 8
- 5 × 3 = 15 and 5 + 3 = 8 ✓
- Factors: (m + 5)(m + 3) = 0
- Solutions: m = -5 or m = -3

Problem 14: n² + 12n + 20 = 0
- Need two numbers that multiply to 20 and add to 12
- 10 × 2 = 20 and 10 + 2 = 12 ✓
- Factors: (n + 10)(n + 2) = 0
- Solutions: n = -10 or n = -2

Problem 15: p² + 9p + 18 = 0
- Need two numbers that multiply to 18 and add to 9
- 6 × 3 = 18 and 6 + 3 = 9 ✓
- Factors: (p + 6)(p + 3) = 0
- Solutions: p = -6 or p = -3

Problem 16: q² + 12q + 32 = 0
- Need two numbers that multiply to 32 and add to 12
- 8 × 4 = 32 and 8 + 4 = 12 ✓
- Factors: (q + 8)(q + 4) = 0
- Solutions: q = -8 or q = -4

Final Answer:
2) a = -6 or -1
3) b = -2
4) c = -3 or -2
5) d = -6 or -2
6) e = -4 or -2
7) f = -5 or -2
8) g = -7 or -1
9) h = -9 or -1
10) i = -4
11) j = -4 or -3
12) k = -8 or -2
13) m = -5 or -3
14) n = -10 or -2
15) p = -6 or -3
16) q = -8 or -4