Factor a^3+a^2b+a+b

$a^{3} + a^{2} b + a + b$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(a^{3} + a^{2} b) + a + b$

Factor out the greatest common factor (GCF) from each group.

$a^{2} (a + b) + 1 (a + b)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $a + b$ .

$(a + b) (a^{2} + 1)$