質問: x ^8+x^4+1 PTĐTTNT
回答: Đáp án: $(x^2 + x + 1)(x^2 – x + 1)(x^4 – x^2 + 1)$ Giải thích các bước giải: $\begin{array}{l}x^8 + x^4 + 1\\ =x^8 + x^7 + x^6 – x^7 – x^6 – x^5 + x^5 + x^4 + x^3 – x^3 – x^2 – x + x^2 + x + 1\\ = x^6(x^2 + x + 1) – x^5(x^2 + x + 1) + x^3(x^2 +x + 1) – x(x^2 +x +1) + (x^2 + x + 1)\\ = (x^2 +x +1)(x^6 – x^5 + x^3 – x + 1)\\ = (x^2 + x + 1)(x^6 – x^5 + x^4 – x^4 + x^3 – x^2 + x^2 – x + 1)\\ = (x^2 + x + 1)[x^4(x^2 – x + 1) – x^2(x^2 – x + 1) + (x^2 – x + 1)]\\ = (x^2 + x + 1)(x^2 – x + 1)(x^4 – x^2 + 1)\end{array}$