Question

phân tích thành nhân tử :

a) x^4 - 3x^2 + 1

b) x^4 - x^2 + 2x

c) x^4 + x^2 + 1

Answer 1

a) x^4 - 3x^2 + 1

=x⁴-2x²+1-x²

=(x²-1)²-x²

=(x²-x-1)(x²+x-1)

 

Answer 2

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

b/ \(=x\left(x^3-x+2\right)\)

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