Question

Phân tích đa thức thành nhân tử 

     x mũ 4-7x mũ 3+14.x mũ 2-7x +1

     x mũ 4+x mũ 3-x -1

Answer 1

\(x^4-7x^3+14x^2-7x+1\\ =\left(x^4-3x^3+x^2\right)+\left(-4x^3+12x^2-4x\right)+\left(x^2-3x+1\right)\\ =x^2\left(x^2-3x+1\right)-4x\left(x^2-3x+1\right)+\left(x^2-3x+1\right)\\ =\left(x^2-3x+1\right)\left(x^2-4x+1\right)\)

Answer 2

\(x^4-7x^3+14x^2-7x+1\)

\(=\left(x^4-4x^3+x^2\right)-\left(3x^3-12x^2+3x\right)+\left(x^2-4x+1\right)\)

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

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

Answer 3

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