Question

Phân tích đa thức thành nhân tử

x^5 + x + 1

 

 

Answer 1

x⁵ + x + 1

= x⁵ - x² + x² + x + 1

= (x⁵ - x²⁾ + (x² + x + 1)

= x²(x³ - 1) + (x² + x + 1)

= x²(x - 1)(x² + x + 1) + (x² + x + 1)

= (x³ - x²)(x² + x + 1) + (x² + x + 1)

= (x² + x + 1)(x³ - x² + 1)

Answer 2

\(x^5+x+1\)

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

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

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

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

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

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