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

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

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

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

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

Factor $x^{2}$ out of $- 2 x^{3}$ .

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

Multiply by $1$ .

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

Factor $x^{2}$ out of $x^{2} x^{2} + x^{2} (- 2 x)$ .

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

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

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

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

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

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 x = 2 \cdot x \cdot 1$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 1$ .

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