Question

PHÂN TÍCH:

a) x^2 - 2x - 4y^2 - 4y

b) x^3 - 4x^2 + 12x - 27

c) (x^2 - 3)^2 + 16

d) x^4 - 2x^3 + 2x -1

e) x^4 + 2x^3 -4x -4

Answer 1

a) x²- 2x - 4y² - 4y = (x² - 2x + 1) - (4y² + 4y + 1) = (x - 1)² - (2y + 1)² = (x - 1 - 2y - 1)(x - 1 + 2y + 1) = (x - 2y - 2)(x + 2y)

b) x³ - 4x² + 12x - 27 = (x³ - 3x²) - (x² - 3x) + (9x - 27) = x²(x - 3) - x(x - 3) + 9(x - 3) = (x² - x + 9)(x - 3)

d) x⁴ - 2x³ + 2x - 1 = (x⁴  - 2x³ + x²) - (x² - 2x + 1) = (x² - x)² - (x - 1)² = (x² - x - x + 1)(x² - x + x - 1)

= (x² - 2x + 1)(x² - 1) = (x - 1)²(x - 1)(x + 1) = (x - 1)³(x + 1)

e) x⁴ + 2x³ - 4x - 4 = (x⁴ + 2x⁴ + x²) - (x² + 4x + 4) = (x² + x)² - (x + 2)² = (x² + x - x - 2)(x²  + x + x + 2) = (x² - 2)(x² + 2x + 2)