Question

phân tích đa thức thành nhân tử: \(x^8+x+1\)

Answer 1

x⁸ + x + 1

= (x⁸ + x⁷ + x⁶) + (- x⁷ - x⁶ - x⁵) + (x⁵ + x⁴ + x³) + (- x⁴ - x³ - x²) + (x² + x + 1)

= (x² + x + 1)(x⁶ - x⁵ + x³ - x² + 1)

Answer 2

\(x^8+x+1\)

\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)

\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+x^2+x+1\)

\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)