How do you factor x3 + x2 + x + 1 by grouping?

We have to factorise \(x^{3}+ x^{2}+ x + 1\) by grouping

Solution

First, group the two terms on the left and the two terms on the right as

\([x^{3}+ x^{2}]+ [x + 1]\)

Now, factor out an x2 from the term on the left, we get

\(x^{2} (x + 1) + (x + 1)\)

Taking out (x+1) as common factor we get

\((x + 1) (x^{2} + 1)\)

Answer

On factorising \(x^{3}+ x^{2}+ x + 1\) by grouping we get \((x + 1) (x^{2} + 1)\)

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