Question

phân tích đa thức thành nhân tử:

a) x³-x²-4

b) x⁴-64

c) 81x⁴+4y⁴

d)x⁷-x²-1

Answer 1

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

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

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

b) \(x^4-64=\left(x^2-8\right)\left(x^2+8\right)\)

c)  \(81x^4+4y^4=\left(9x^2+2y^2\right)^2-36x^2y^2=\left(9x^2-6xy+2y^2\right)\left(9x^2+6xy+2y^2\right)\)

d)  \(x^7-x^2-1=\left(x^2-x+1\right)\left(x^5+x^4-x^2-x-1\right)\)