Question

Phân tích đa thức thành nhân tử:  \(\left(x^2-x+2\right)^2+\left(x-2\right)^2.\)

Answer 1

\(\left(x^2-x+2\right)^2+\left(x-2\right)^2\)

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

\(=\left(x^2-x+2+x-2\right).\left(x^2-x+2-x+2\right)\)

Answer 2

Ta có BT =\(x^4-2x^3+6x^2-8x+8=x^4+4x^2-2x^3-8x+2x^2+8=x^2\left(x^2+4\right)-2x\left(x^2+4\right)+2\left(x^2+4\right)\)

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