Question

phan tich thanh nhan tu:

\(x^8+x+1\)

Answer 1

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

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

Answer 2

Ta có: x⁸ + x + 1

= x⁸ - x⁵ + x⁵ - x² + x² + x + 1

= (x⁸ - x⁵) + (x⁵ - x²) + x² + x + 1

= x⁵(x³ - 1) + x²(x³ - 1) + x² + x + 1

= (x³ - 1)(x⁵ + x²) + x² + x + 1

= (x - 1)(x² + x + 1)(x⁵ + x²) + x² + x + 1

= x⁵(x - 1)(x² + x + 1) + x²(x - 1)(x² + x + 1)

= (x⁶ - x⁵)(x² + x + 1) + (x³ - x²)(x² + x + 1) + (x² + x + 1)

= (x² + x + 1)(x⁶ - x⁵ + x³ - x² + 1)