Question

Phân tích đa thức thành nhân tử bằng cách kết hợp nhiều phương pháp

a) x² . (x - 3) + 12 - 4x

b) x² - 4 + (x - 2)²

c) x³ - 4x² - 12x + 27

Làm rõ từng bước giúp e nhé! Thanks nhìu ạ !

 

Answer 1

a) \(x^2\left(x-3\right)+12-4x=x^2\left(x-3\right)-4x+12\)

\(=x^2\left(x-3\right)-4\left(x-3\right)\)

\(=\left(x-3\right)\left(x^2-4\right)\)

\(=\left(x-3\right)\left(x^2-2^2\right)\)

\(=\left(x+3\right)\left(x-2\right)\left(x+2\right)\)

b)\(x^2-4+\left(x-2\right)^2=x^2-2^2+\left(x-2\right)^2\)

\(=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\)

\(=\left(x-2\right)\left(x+2+x-2\right)\)

\(=\left(x-2\right)2x\)

c)\(x^3-4x^2-12x+27=x^3+3x^2-7x^2-21x+9x+27\)

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

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

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

Answer 2

a) => x².(x-3)-4(x-3)=(x-3)(x²-4)=(x-3)(x-2)(x+2)

b) => (x+2)(x-2)+(x-2)²=(x-2)(x+2+x-2)=2x(x-2)

c) => x³+27-(4x²+12x)=(x+3)(x²-3x+3)-4x(x+3)=(x+3)(x²-3x+3-4x)=(x-3)(x²-7x+3)