Question

Phân tích đa thức thành nhân tử:

x¹¹ + x¹⁰  + ....... + x² + x + 1

Answer 1

\(=x^{10}\left(x+1\right)+x^8\left(x+1\right)+...+x^4\left(x+1\right)+x^2\left(x+1\right)+\left(x+1\right)\)

\(=\left(x+1\right)\left(x^{10}+x^8+x^6+x^4+x^2+1\right)\)

\(=\left(x+1\right)\left(x^2+1\right)\left(x^8+x^4+1\right)\)

\(=\left(x+1\right)\left(x^2+1\right)\left[x^8+2x^4+1-x^4\right]\)

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

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

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

Answer 2

 x¹¹ + x¹⁰  +  x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + x² + x + 1

= x¹⁰( x + 1) + x⁸( x + 1) + x⁶( x + 1) + x⁴( x + 1) + x²( x + 1) + ( x + 1)

= (x+1).(x¹⁰ + x⁸ + x⁶ + x⁴ + x² + 1)

=(x+1).[x⁸.(x² + 1) + x⁴.(x + 1) + (x² + 1)]

=(x+1).(x² + 1).(x⁸ + x⁴ + 1)