Question

phân tích đa thức thành nhân tử
\(4x^5+x\)

Answer 1

\(4x^5+x\)
\(=x\left(4x^4+1\right)\)
\(=x\left[\left(2x^2\right)^2+1^2\right] \)
\(=x\left[\left(2x^2\right)+2.2x^2.1+1^2\right]-2.2x^2.1\)
\(=x\left(2x^2+1\right)^2-4x^2\)
\(=x\left(2x^2+1-4x\right)\left(2x^2+1+4x\right)\)

Answer 2

\(4x^5+x=x\left(4x^4+1\right)\)

Answer 3

\(4x^5+x=x\left(4x^2+1\right)\)

\(=x\left[\left(2x\right)^2+2\cdot2x\cdot1+1^2-2\cdot2x\cdot1\right]\)

\(=x\left[\left(2x+1\right)^2-4x\right]\)

\(=x\left[\left(2x+1\right)^2-\left(2\sqrt{x}\right)^2\right]\)

\(=x\left(2x-2\sqrt{x}+1\right)\left(2x+2\sqrt{x}+1\right)\)