Question

Phân tích đa thức sau thành nhân tử: x^2.(x^4-1).(x^2+2)+1

Answer 1

Ta có: \(x^2\left(x^4-1\right)\left(x^2+2\right)+1\)

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

\(=x^8+2x^6-x^4-2x^2+1\)

\(=x^8+x^6-x^4+x^6+x^4-x^2-x^4-x^2+1\)

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

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