Using factor theorem, factorize each of the following polynomials : `x^3+2x^2-x-2`

Explanation

`p(x)=x^3+2x^2-x-2`
Factors of -2 are `+-1,+-2`.
`p(1)=1+2-1-2=0`
By trial and error, 1 is a zero of p(x)
So by factor theorem,`x-1` is a factor of p(x).
`p(x)=x^3+2x^2-x-2`
`=x^3-x^2-3x+2x-2`
`=x^2(x-1)+3x(x-1)+2(x-1)`
`=(x^2+2x+x+2)(x-1)`
`=[x(x+2)+1(x+2)](x-1)`
`=(x+1)(x+2)(x-1)`