Question

Phân tích đa thức sau thành nhân tử:     x^5 + x +1

Answer 1

tớ thử nha

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 2

Ta có:\(x^5+x+1\)

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

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

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

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

Answer 3

\(x^5+x+1\)

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

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

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

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

Answer 4

x5+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)