Question

Phân tích đa thức thành nhân tử:

a) x² - x - 2
b) x³ - 19x - 30
c) x³ - 6x² + 11x - 6

Answer 1

a) \(x^2-x-2=x^2+x-2x-2=x\left(x+1\right)-2\left(x+1\right)\)

\(=\left(x+1\right)\left(x-2\right)\)

Answer 2

a) \(x^2-x-2=x^2-2x+x-2=x\left(x-2\right)+\left(x-2\right)=\left(x-2\right)\left(x+1\right)\)

b) \(x^3-19x-30==x^3+2x^2-2x^2-4x-15x-30=x^2\left(x+2\right)-2x\left(x+2\right)-15\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2+2x-15\right)=\left(x+2\right)\left(x-3\right)\left(x+5\right)\)

c) \(x^3-6x^2+11x-6=x^3-x^2-5x^2+5x+6x-6=x^2\left(x-1\right)-5x\left(x-1\right)+6\left(x-1\right)=\left(x-1\right)\left(x-2\right)\left(x-3\right)\)

Answer 3

a)x²-x-2=x²-2x+x-2=x(x-2)+(x-2)=(x-2)(x+1)

b)x³-19x-30=x³+2x²-2x²-4x-15x-30=x²(x+2)-2x(x+2)-15(x+2)=(x²-2x-15)(x+2)=(x²+3x-5x-15)(x+2)=[x(x+3)-5(x+3)](x+2)=(x-5)(x+3)(x+2)=(x-5)(x+2)(x+3)

c)x³-6x²+11x-6=x³-x²-5x²+5x+6x-6=x²(x-1)-5x(x-1)+6(x-1)=(x²-5x+6)(x-1)=(x²+x-6x+6)(x-1)=[x(x+1)-6(x+1)](x-1)=(x-6)(x+1)(x-1)=(x-6)(x-1)(x+1)