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

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

Step 1

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

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

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

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

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

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

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

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

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

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

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

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

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

Step 2

Factor using the perfect square rule.

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

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

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.

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

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

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