Factor x^3-12x^2+36x

$x^{3} - 12 x^{2} + 36 x$

Step 1

Factor $x$ out of $x^{3} - 12 x^{2} + 36 x$ .

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

$x \cdot x^{2} - 12 x^{2} + 36 x$

Factor $x$ out of $- 12 x^{2}$ .

$x \cdot x^{2} + x (- 12 x) + 36 x$

Factor $x$ out of $36 x$ .

$x \cdot x^{2} + x (- 12 x) + x \cdot 36$

Factor $x$ out of $x \cdot x^{2} + x (- 12 x)$ .

$x (x^{2} - 12 x) + x \cdot 36$

Factor $x$ out of $x (x^{2} - 12 x) + x \cdot 36$ .

$x (x^{2} - 12 x + 36)$

Step 2

Factor using the perfect square rule.

Rewrite $36$ as $6^{2}$ .

$x (x^{2} - 12 x + 6^{2})$

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

$12 x = 2 \cdot x \cdot 6$

Rewrite the polynomial.

$x (x^{2} - 2 \cdot x \cdot 6 + 6^{2})$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 6$ .

$x {(x - 6)}^{2}$