phân tích nhé x mũ 5 + x mũ 4 +1 x mũ 5 + x +1 x mũ 8 + x mũ 7 +1 x mũ 8 + x +1

Đáp án:

Giải thích các bước giải:

x^5 + x^4 + 1 = (x^5 + x^4 + x^3) – (x^3 – 1)

= x^3(x^2 + x + 1) – (x – 1)(x^2  +x + 1) = (x^2 + x + 1)(x^3 – x + 1)

x^5 + x + 1 = x^5 + x^4 – x^4 + x^3 – x^3 + x^2 – x^2 + x + 1

= x^5 + x^4 + x^3 – x^4 – x^3 – x^2 + x^2 + x + 1

= x^3(x^2  +x + 1) – x^2(x^2 + x + 1) + (x^2 + x + 1)

= (x^2  +x + 1)(x^3 – x^2 + 1)

x^8 + x^7 + x^1 = (x^8 – x^2) + (x^7 – x) + (x^2 + x + 1) = (x^2 + x)(x^6 – 1) + (x^2  + x + 1)

= (x^2 + x)(x^3 + 1)(x – 1)(x^2 + x + 1) + (x^2 + x + 1)

= (x^2 + x + 1)[(x^2 + x)(x^3 + 1)(x – 1) + 1] = (x^2 +x + 1)(x^6 – x^4 + x^3 – x + 1)

Đặt A =  x^8 + x + 1 = (x^8 – x^2) + (x^2 + x + 1) = x^2(x^6 – 1) + (x^2 + x + 1)

Ta có : x^6 – 1 = (x^3 + 1)(x^3 – 1) = (x^3 + 1)(x – 1)(x^2 +x + 1)

Thay vào A được : A = x^2(x^3 + 1)(x – 1)(x^2 + x + 1) + (x^2 + x + 1)

= (x^2 + x + 1)[x^2(x^3 + 1)(x – 1) + 1] = (x^2 + x + 1)(x^6 – x^5 + x^3 – x^2 + 1)