Question

phân tích đa thức thành nhân tử:

a,x^3-4x^2+4x-xy^2

b,x^3 -4x^2 +121x-27

c,3x^2 -7x -10

d,5x^3 -5x^2y -10x^2 +10xy

Answer 1

a) x³ - 4x² + 4x - xy²

= x(x² - 4x + 4 - y²)

= \(x\left [ (x - 2)^{2} - y^{2}\right ]\)

= x(x - 2 - y)(x - 2 + y)

c) 3x² - 7x - 10

= 3x² + 3x - 10x - 10

= 3x(x + 1) - 10(x + 1)

= (x + 1)(3x - 10)

d) 5x³ - 5x²y - 10x² + 10xy

= 5x(x² - xy - 2x + 2y)

= \(5x\left [ x(x - y) - 2(x - y) \right ]\)

= 5x(x - y)(x - 2)

b) sửa đề: x³ - 4x² + 12x - 27

= x³ - 27 - 4x² + 12x

= (x - 3)(x² + 3x + 9) - 4x(x - 3)

= (x - 3)(x² + 3x - 4x + 9)

= (x - 3)(x² - x + 9)