Question

Factor x3 + x2 + x + 1 by grouping. What is the resulting expression? (x2)(x + 1) (x2 + 1)(x) (x2 + 1)(x + 1) (x3 + 1)(x + 1)

Answer 1

Answer :$(x^2 + 1)( x + 1)$

Factor $x^3 + x^2 + x + 1$ by grouping

We group first two terms and last two terms

$(x^3 + x^2)+( x + 1)$

Now we take out GCF from each group

GCF of $(x^3 + x^2)$ is x^2

GCF of $+( x + 1)$ is 1

$(x^3 + x^2) +( x + 1)$

$x^2(x + 1) +1( x + 1)$

Now we factor out x+1 that is in common

$(x^2 + 1)( x + 1)$

Answer 2

Group and factor out the greatest common factor (GCF), then combine.

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