Question

Phân tích đa thức thành nhân tử 

x⁵ + x + 1

Answer 1

Ta có:  x^5 + x + 1 =  x^5 - x^2 + x^2 + x +1

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

                              =  x^2(x-1)(x^2 + x + 1) + (x^2 + x + 1)

                              =  (x^2 + x + 1)[x^2(x-1)+1]

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

Answer 2

lam theo Le Huu Minh chien hoac ban cu lam cach nay la ra voi moi bai dang x^a+x+1

x⁵+x+1=x⁵+x⁴+x³-x⁴-x³-x²+x²+x+1=x³.(x²+x+1)-x².(x²+x+1)+(x²+x+1)=(x²+x+1).(x³-x²+1)

Answer 3

\(x^5+x+1\)

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

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

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

\(\left(x^2+x+1\right)\left[x^2\left(x-1\right)+1\right]\)