Question

phân tích đa thức thành nhân tử.

x^5 + x +1

Thanks!!!

Answer 1

Ta có:

x^5+x+1=(x^3+x^2)+x+1=x^2(x+1) + (x+1) =(x+1)(x^2+1)

Answer 2

\(=x^5+x+1=x^5-x^4+x^4-x^3+x^3-x^2+x^2+x+1\)

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

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

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