Question

factor $x^3 + x^2 + x + 1$ by grouping. what is the resulting expression?\
$\bigcirc$ $(x^2)(x + 1)$\
$\bigcirc$ $(x^2 + 1)(x)$\
$\bigcirc$ $(x^2 + 1)(x + 1)$\
$\bigcirc$ $(x^3 + 1)(x + 1)$

Explanation:

Step1: Group terms into pairs

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

Step2: Factor out GCF from each pair

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

Step3: Factor out common binomial

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

Answer:

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