Question

Phân tích đa thức thành nhân tử:

1) \(x^{12}+x^6+1\)

2) \(x^{4n}+5x^{2n}+9\)

3) \(2bc\left(b+2c\right)+2ac\left(c-2a\right)-2ab\left(a+2b\right)-7abc\)

Answer 1

a)\(x^{12}+x^6+1=x^{12}+2x^6+1-x^6=\left(x^6+1\right)^2-x^6\)
\(=\left(x^6+1\right)^2-\left(x^3\right)^2=\left(x^6-x^3+1\right)\left(x^6+x^3+1\right)\).

Answer 2

b) \(x^{4n}+5x^{2n}+9=x^{4n}+6x^{2n}+9-x^{2n}=\left(x^{2n}+3\right)^2-x^{2n}\)
\(=\left(x^{2n}-x^n+3\right)\left(x^{2n}+x^n+3\right)\).