Question

Phân tích đa thức thành nhân tử bằng phương pháp tách: a) x^2-4x-5 b)x^3+3x^2+3x+2 c)x^3+x^2-x+2 d)2x^2-5xy+3y^2 e)x^4-5x^2+4

Answer 1

a, \(x^2-4x-5\)

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

\(=x\left(x-5\right)+\left(x-5\right)=\left(x-5\right)\left(x+1\right)\)

b, \(x^3+3x^2+3x+2\)

\(=x^3+2x^2+x+2x+x+2\)

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

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

c, \(x^3+x^2-x+2\)

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

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

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

d, \(2x^2-5xy+3y^2\)

\(=2x^2-2xy-3xy+3y^2\)

\(=2x\left(x-y\right)-3y\left(x-y\right)\)

\(=\left(x-y\right)\left(2x-3y\right)\)

e, \(x^4-5x^2+4\)

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

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

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

Chúc bạn học tốt!!!