Since both ExplainAnswer and TeachTopic are false, I will proceed directly to solving the problems and providing the final answers.
Let me work through each problem systematically:
Section A:
1) (x + 2)(x + 3) = 0
- Set each factor equal to zero: x + 2 = 0 or x + 3 = 0
- x = -2 or x = -3
2) (4x + 3)(x - 3) = 0
- Set each factor equal to zero: 4x + 3 = 0 or x - 3 = 0
- 4x = -3, so x = -3/4 or x = 3
3) (2x - 5)(3x + 2) = 0
- Set each factor equal to zero: 2x - 5 = 0 or 3x + 2 = 0
- 2x = 5, so x = 5/2 or 3x = -2, so x = -2/3
4) (4x + 8)(2x - 8) = 0
- Set each factor equal to zero: 4x + 8 = 0 or 2x - 8 = 0
- 4x = -8, so x = -2 or 2x = 8, so x = 4
5) (5x - 15)(4x - 2) = 0
- Set each factor equal to zero: 5x - 15 = 0 or 4x - 2 = 0
- 5x = 15, so x = 3 or 4x = 2, so x = 1/2
6) (9x - 12)(5x + 20) = 0
- Set each factor equal to zero: 9x - 12 = 0 or 5x + 20 = 0
- 9x = 12, so x = 12/9 = 4/3 or 5x = -20, so x = -4
Section B:
1) x² + 8x + 15 = 0
- Factor: (x + 3)(x + 5) = 0
- x = -3 or x = -5
2) x² - 7x + 12 = 0
- Factor: (x - 3)(x - 4) = 0
- x = 3 or x = 4
3) x² + 2x - 15 = 0
- Factor: (x + 5)(x - 3) = 0
- x = -5 or x = 3
4) x² - 11x + 28 = 0
- Factor: (x - 4)(x - 7) = 0
- x = 4 or x = 7
5) x² - x - 30 = 0
- Factor: (x - 6)(x + 5) = 0
- x = 6 or x = -5
6) x² + 11x - 26 = 0
- Factor: (x + 13)(x - 2) = 0
- x = -13 or x = 2
7) x² - 5x - 24 = 0
- Factor: (x - 8)(x + 3) = 0
- x = 8 or x = -3
8) 14 + x² + 9x = 0
- Rearrange: x² + 9x + 14 = 0
- Factor: (x + 7)(x + 2) = 0
- x = -7 or x = -2
9) 7 + x² - 8x = -25
- Rearrange: x² - 8x + 32 = 0
- Factor: (x - 4)(x - 8) = 0
- x = 4 or x = 8
10) x² = 17x - 72
- Rearrange: x² - 17x + 72 = 0
- Factor: (x - 8)(x - 9) = 0
- x = 8 or x = 9
Final Answer:
Section A: 1) x = -2, -3 2) x = -3/4, 3 3) x = 5/2, -2/3 4) x = -2, 4 5) x = 3, 1/2 6) x = 4/3, -4
Section B: 1) x = -3, -5 2) x = 3, 4 3) x = -5, 3 4) x = 4, 7 5) x = 6, -5 6) x = -13, 2 7) x = 8, -3 8) x = -7, -2 9) x = 4, 8 10) x = 8, 9
Parent Tip: Review the logic above to help your child master the concept of factoring and solving quadratics worksheet.
