Question

phân tích đa thức thành nhân tử : x⁴+4x²-5

Answer 1

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

Answer 2

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

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

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

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

Answer 3

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

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

Answer 4

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

\(=\left(x^2\right)^2+2.x^2.2+2^2-9\)

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

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

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