Question

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

Answer 1

Ta có: \(x^5+x+1\)

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

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

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

Answer 2

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

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

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

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

Answer 3

\(x^5+x+1\)

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

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

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

Answer 4

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^3-x^2+1)