Question

Phân tích đa thức => nhan tử giải chi tiết

a) X^3+2x+x

b) -5x^2+10x-5y+5

c) 4x^3-8x^2y+4xy^2

d) x^3+9x^2y-xy

Answer 1

\(x^3+2x^2+x=x\left(x^2+2x+1\right)=x\left(x+1\right)^2\)

\(5x^2+10x-5y^2+5==5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y^2\right]=5\left(x+1-y\right)\left(x+1+y\right)\)

\(4x^3-8x^2y+4xy^2=4x\left(x^2-2xy+y^2\right)=4x\left(x-y\right)^2\)

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

Answer 2

a) \(x^3+2x^2+x=x\left(x^2+2x+1\right)=x\left(x+1\right)^2\)

b) \(-5x^2+10x-5y+5=-5\left(x^2-2x+y-1\right)\)

c)\(4x^3-8x^2y+4xy^2=4x\left(x^2-2xy+y^2\right)=4x\left(x-y\right)^2\)

d) \(x^3+9x^2y-xy=x\left(x^2+9xy-y\right)\)