Question

x^3+x+2  ;,x^3+3x^2-4 phan tich da thuc sau thành nhân tử

Answer 1

\(x^3+x+2\)

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

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

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

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

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

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

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

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

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

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