Question

x⁴+5x³-2x²+10x+4

Answer 1

\(x^4+5x^3-2x^2+10x+4\)

\(=\left(x^4+4\right)+\left(5x^3+10x\right)-2x^2\)

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

\(=\left(x^2+2\right)^2+5x\left(x^2+2\right)-6x^2\)

Đặt \(x^2+2=a\). Khi đó đa thức có dạng :

\(a^2+5xa-6x^2\)

\(=a^2-xa+6xa-6x^2\)

\(=a\left(a-x\right)+6x\left(a-x\right)\)

\(=\left(a-x\right)\left(a+6x\right)\)

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