Question

Phân tích đa thức sau thành nhân tử:

x⁵ + x - 1

Answer 1

\(x^5+x-1\)

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

\(=\left(x^5-x^4+x^3\right)+\left(x^4-x^3+x^2\right)-\left(x^2-x+1\right)\)

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

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

Answer 2

Ủng hộ cách khác:v

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