Question

Bài 4 : Phân tích các đa thức thành nhân tử :
a, x^5 - x^4 - x^3 - x^2 - x - 2
b, x^9 - x^7 - x^6 - x^5 + x^4 + x^3 + x^2 - 1
Giúp mk vs ạ mk đang cần gấp ạ

Answer 1

Bài 4:

a) Ta có: \(x^9-x^7-x^6-x^5+x^4+x^3+x^2-1\)

\(=\left(x^9-x^7\right)-\left(x^6-x^4\right)-\left(x^5-x^3\right)+\left(x^2-1\right)\)

\(=x^7\left(x^2-1\right)-x^4\left(x^2-1\right)-x^3\left(x^2-1\right)+\left(x^2-1\right)\)

\(=\left(x^2-1\right)\left(x^7-x^4-x^3+1\right)\)

\(=\left(x^2-1\right)\cdot\left[x^4\left(x^3-1\right)-\left(x^3-1\right)\right]\)

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

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

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

Answer 2

a, Ta có : \(x^5-x^4-x^3-x^2-x-2\)

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

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

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