Question

Phân tích đa thức sau thành nhân tử : 

a) \(x^{12}-3x^6+1\)

b)\(x^4+6x^3+7x^2-6x+1\)

c)\(x^5-x^4-x^3-x^2-x-2\)

 

Answer 1

a) \(x^{12}-3x^6+1\)

\(=\left(x^6\right)^2-2\cdot x^6\cdot1+1^2-x^6\)

\(=\left(x^6-1\right)^2-\left(x^3\right)^2\)

\(=\left(x^6-x^3-1\right)\left(x^6+x^3-1\right)\)

Answer 2

b) \(x^4+6x^3+7x^2-6x+1\)

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

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

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

Answer 3

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

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

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

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