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Question

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


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Solution

Factorize using the grouping method

The given expression is x3+x2+x+1.

Follow the below steps to factorize an equation of the above form:

  • Group two pairs of terms.
  • Factor out the common terms from each group.
  • Factor out the common group so obtained.

Then, the given expression can be factorized as follows,

x3+x2+x+1=x3+x2+x+1

x3+x2+x+1=x2x+1+1x+1 [ab+ac=a(b+c)]

x3+x2+x+1=x+1x2+1

Hence, the factors of x3+x2+x+1 obtained by using the common factor method is x+1x2+1.


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