Question

Phân tích đa thức thành nhân tử:

1. \(4\left(x+5\right)\left(x+6\right)\left(x+10\right)\left(x+12\right)-3x^2\\ \)

2. \(x^2-x-1991.1992\)

3. \(x^4-3x^2+4x-3\)

Answer 1

1. 4 (x+5) (x+6) (x+10) (x+12) - 3x² = A

= 4 (x+5) (x+12) (x+6) (x+10) - 3x²

= 4 (x² +17x +60) (x² +16x +60) - 3x²

Đặt a = x² +16x +60 => x² +17x +60 = a +x

A = 4 . a . (a+x) -3x²

= 4a² + 4ax - 3x²

= (2a)² + 2. 2a . x + x² - 4x²

= (2a + x)² - 4x²

= (2a + x - 2x) (2a + x +2x)

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

= [ 2 . (x² +16x +60) - x ]. [ 2. (x² +16x +60) +3x]

= ( 2x² +31x +120) (2x² + 35x + 120)