Phân tích đa thức thành nhân tử: x^10 + x^5 + 1
Giải thích
x10 + x5 + 1
= x10 – x + x5 - x2 + x2 + x + 1
= x.(x9 - 1) + x2.(x3 - 1) + (x2 + x + 1)
= x.(x3 - 1)(x3 + 1) + x2(x3 - 1) + (x2 – x + 1)
= x.(x - 1)(x2 + x + 1)(x3 + 1) + x2(x - 1)(x2 + x + 1) + (x2 + x + 1)
= (x2 + x + 1)[x.(x - 1)(x3 + 1) + x2(x - 1) + 1]
= (x2 + x + 1)(x5 + x2 - x4 – x + x3 - x2 + 1)
= (x2 + x + 1)(x5 - x4 + x3 – x + 1)