Verified answer

32) (2 + 3x + x²)(12 + 7x + x²) = 0

(x² + 3x + 2)(x² + 7x + 12) = 0

(x + 2)(x + 1)(x + 3)(x + 4) = 0

x + 2 = 0       x + 1 = 0       x + 3 = 0    x + 4 = 0

x₁ = - 2           x₂ = - 1         x₃ = - 3       x₄ = - 4

3) (1 - 2x² + x)(5 - 10,5x + x²) = 0

( - 2x² + x + 1)(x² - 10,5x + 5) = 0

- 2x² + x + 1 = 0

2x² - x - 1 = 0

D = (-1)² - 4 * 2 * (- 1) = 1 + 8 = 9 = 3²

4) (12 - 7x + x²)(5x - 1 - 6x²) = 0

(x² - 7x + 12)(- 6x² + 5x - 1) = 0

x² - 7x + 12 = 0

x₁ = 3       x₂ = 4

- 6x² + 5x - 1 = 0

6x² - 5x + 1 = 0

D = (- 5)² - 4 * 6 * 1 = 25 - 24 = 1