Question

Phân tích các đa thức sau thành nhân tử:
a) xy²-25x
b) x(x-y)2x-2y
c) x³-3x²-4x+12

Answer 1

a) \(xy^2-25x=x\left(y^2-25\right)=x\left(y-5\right)\left(y+5\right)\)

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

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

Answer 2

\(a,=x\left(y^2-25\right)=x\left(y-5\right)\left(y+5\right)\\ b,=x\left(x-y\right)+2\left(x-y\right)=\left(x+2\right)\left(x-y\right)\\ c,=x^2\left(x-3\right)-4\left(x-3\right)=\left(x-2\right)\left(x+2\right)\left(x-3\right)\)

Answer 3

\(x\left(y^2-25\right)=y\left(y-5\right)\left(y+5\right)\)

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

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