Question

Phân tích các đa thức sau thành nhân tử :

a) \(x^2-4+\left(x-2\right)^2\)

b) \(x^3-2x^2+x-xy^2\)

c) \(x^3-4x^2-12x+27\)

Answer 1

a) x² – 4 + (x – 2)²

= (x² – 2²) + (x – 2)² = (x – 2)(x + 2) + (x – 2)²

= (x – 2) [(x + 2) + (x – 2)]

= (x – 2)(x + 2 + x – 2)

= 2x(x – 2)

b) x³ – 2x² + x – xy²

= x(x² – 2x + 1 – y²) = x[(x² – 2x + 1) – y2]

= x[(x – 1)2 – y2]

= x[(x – 1) + y] [(x – 1) – y]

= x(x – 1 + y)(x – 1 – y)

c) x³ – 4x² – 12x + 27

= (x³ + 27) – 4x(x + 3)

= (x + 3)(x² – 3x + 9) – 4x(x + 3)

= (x + 3)(x² – 3x + 9 – 4x)

= (x + 3)(x² – 7x + 9)

Answer 2

Answer 3

a) $x^2-4+{\left(x-2\right)}^2$

=x²-2²+(x-2)²

= (x-2)(x+2)+(x-2)²

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

= (x-2)2x

b) $x^3-2x^2+x-x{y}^2$

= x(x²-2x+1-y²)

= x[(x²-2x+1)-y²]

=x[(x-1)²-y²]

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

c) $x^3-4x^2-12x+27$

$\mathrm{=x3+3x2-7x2-21x+9x+27}$

$\mathrm{=(x3+3x2)-(7x2+21x)+(9x+27)}$

=x²(x+3)-7x(x-3)+9(x+3)

=(x+3)(x2-7x+9)