Question

Phân tích đa thức thành nhân tử:

\(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)

Answer 1

\(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)

\(=3x^4+3x^2+3-\left(x^4+x^2+1+2x^3+2x^2+2x\right)\)

\(=3x^4+3x^2+3-x^4-x^2-1-2x^3-2x^2-2x\)

\(=2x^4-2x^3-2x+2\)

\(=2x^3.\left(x-1\right)-2.\left(x-1\right)=\left(x-1\right).\left(2x^3-2\right)\)

\(=2.\left(x-1\right).\left(x^3-1\right)\)

Chúc bạn học tốt!!!

Answer 2

\(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\\ =3\left(x^{2^2}+2x^2+1-x^2\right)-\left(x^2+x+1\right)\\ =3\left(x^2+x+1\right)\left(x^2-x+1\right)-\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(3x^2-3x+3-x^2-x-1\right)\\ =\left(x^2+x+1\right)\left(2x^2-4x+2\right)\\ =2\left(x^2+x+1\right)\left(x-1\right)^2\)