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Answer:
[tex]x^3+x^2+x+1=\left(x+1\right)\left(x^2+1\right)[/tex]
Step-by-step explanation:
Given the expression
[tex]x^3+x^2+x+1[/tex]
Factorized by grouping
[tex]x^3+x^2+x+1=\left(x^3+x^2\right)+\left(x+1\right)[/tex]
Factor out x² from x³+ x²: x²(x+1)
[tex]=\left(x+1\right)+x^2\left(x+1\right)[/tex]
[tex]=\left(x+1\right)+x^2\left(x+1\right)[/tex]
Factor common term x+1
[tex]=\left(x+1\right)\left(x^2+1\right)[/tex]
Therefore, we conclude that:
[tex]x^3+x^2+x+1=\left(x+1\right)\left(x^2+1\right)[/tex]