Question

phân tích đa thức thành nhân tử:

a, x²-4+3c(x-2)

b, x²-2x+xy+1+y

c, x² -y²-4x+4

d, x²-4x+4-25

e,x²+6x-7

Answer 1

a) Sửa đề:

x² - 4 + 3x(x - 2)

= (x² - 4) + 3x(x - 2)

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

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

= (x - 2)(4x + 2)

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

b) Sửa đề

x² + 2x + xy + 1 + y

= (x² + 2x + 1) + (xy + y)

= (x + 1)² + y(x + 1)

= (x + 1)(x + 1 + y)

c) x² - y² - 4x + 4

= (x² - 4x + 4) - y²

= (x - 2)² - y²

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

d) x² - 4x + 4 - 25

= (x² - 4x + 4) - 25

= (x - 2)² - 5²

= (x - 2 - 5)(x - 2 + 5)

= (x - 7)(x + 3)

e) x² + 6x - 7

= x² - x + 7x - 7

= (x² - x) + (7x - 7)

= x(x - 1) + 7(x - 1)

= (x - 1)(x + 7)

Answer 2