Question

X3+x2+x+1 by grouping

Answer 1

`x^3+x^2+x+1=\left(x+1\right)\left(x^2+1\right)`

Explanation:

Given the expression

`x^3+x^2+x+1`

Factorized by grouping

`x^3+x^2+x+1=\left(x^3+x^2\right)+\left(x+1\right)`

Factor out x² from x³+ x²: x²(x+1)

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

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

Factor common term x+1

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

Therefore, we conclude that:

`x^3+x^2+x+1=\left(x+1\right)\left(x^2+1\right)`