How do you factor #x^3+x^2+x+1# by grouping?

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Answer 1 · 2017-03-16T01:54:48

See the entire solution process below:

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 #x^2# from the term on the left to give:

#((x^2 xx x) + (x^2 xx 1)) + (x + 1)#

#x^2(x + 1) + (x + 1)#

#(x + 1)# can also be written as #1(x + 1)# giving:

#x^2(x + 1) + 1(x + 1)#

We can now factor out an #(x + 1)# from each term giving:

#(x + 1)(x^2 + 1)#