Question

Bài 2. (3 điểm) Phân tích các đa thức sau thành nhân tử:

a) 4x² – 6x³y – 2x² + 8x b) x² – 4 – 2xy + y²

c) x³ – 4x² – 12x +27 d) 3x² – 18x + 27

Answer 1

a) 4x² – 6x³y – 2x² + 8x = 2x ( 2x - 3 x\(^2\)y - x + 4 )

b) x2 – 4 – 2xy + y2 = ( x2– 2xy + y2) \(-4\) = ( x - y )\(^2\) - 2\(^2\)

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

c) x³ – 4x² – 12x +27

= (x\(^3\) + 27 ) - ( 4x\(^2\) + 12x )

= ( x + 3 ) ( x\(^2\) - 3x + 9 ) - 4x ( x + 3)

= ( x + 3 ) ( x\(^2\) - 3x + 9 - 4x )

= ( x + 3 ) ( x\(^2\) - 7x + 9 )

d) 3x2 – 18x + 27 = 3 ( x\(^2\) - 6x + 9 )