Factor f(x)=x^4+x^3+x^2+x

$f (x) = x^{4} + x^{3} + x^{2} + x$

Factor $x$ out of $x^{4} + x^{3} + x^{2} + x$ .

Factor $x$ out of $x^{4}$ .

$f (x) = x \cdot x^{3} + x^{3} + x^{2} + x$

Factor $x$ out of $x^{3}$ .

$f (x) = x \cdot x^{3} + x \cdot x^{2} + x^{2} + x$

Factor $x$ out of $x^{2}$ .

$f (x) = x \cdot x^{3} + x \cdot x^{2} + x \cdot x + x$

Raise $x$ to the power of $1$ .

$f (x) = x \cdot x^{3} + x \cdot x^{2} + x \cdot x + x$

Factor $x$ out of $x^{1}$ .

$f (x) = x \cdot x^{3} + x \cdot x^{2} + x \cdot x + x \cdot 1$

Factor $x$ out of $x \cdot x^{3} + x \cdot x^{2}$ .

$f (x) = x (x^{3} + x^{2}) + x \cdot x + x \cdot 1$

Factor $x$ out of $x (x^{3} + x^{2}) + x \cdot x$ .

$f (x) = x (x^{3} + x^{2} + x) + x \cdot 1$

Factor $x$ out of $x (x^{3} + x^{2} + x) + x \cdot 1$ .

$f (x) = x (x^{3} + x^{2} + x + 1)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$f (x) = x ((x^{3} + x^{2}) + x + 1)$

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

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

Factor.

Factor the polynomial by factoring out the greatest common factor, $x + 1$ .

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

Remove unnecessary parentheses.

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