Đáp án+Giải thích các bước giải:
`h, x^10 + x^5 + 1`
`= x^10 - x + x^5 - x² + x² + x + 1`
`= (x^10 - x) + (x^5-x²) + (x² + x +1)`
`= x(x^9-1) + x²(x³ - 1) + (x² + x + 1)`
`= x[(x³)³ - 1³] + x² (x³ - 1³) + (x² + x + 1)`
`= x(x³-1)(x^6 + x³ + 1) + x²(x-1)(x² + x + 1) + (x² + x + 1)`
`= x(x-1)(x²+x+1)(x^6 + x³ + 1) + x²(x-1)(x²+x+1) + (x²+x+1)`
`= (x²+x+1) [x(x-1)(x^6 + x³ + 1) + x²(x-1) + 1]`
`= (x² + x + 1) ( x^5 + x^8 + x² - x^7 - x^4 - x + x³ - x² + 1 )`
`= (x² + x + 1) ( x^8 - x^7 + x^5 - x^4 + x³ - x + 1)`
`i) x^5 - x^4 - 1`
`= x^5 - x³ - x² - x^4 + x² + x + x³ - x - 1`
`= (x^5 - x³ - x²) - (x^4 - x² - x) + (x³ - x - 1)`
`= x²(x³ - x - 1) - x(x³ - x - 1) + (x³ - x - 1)`
`= (x³ - x - 1)(x² - x +1)`
