Precalculus Examples

$2 x^{3} - 8 x^{2} + 8 x$

Step 1

Factor $2 x$ out of $2 x^{3} - 8 x^{2} + 8 x$ .

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Step 1.1

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

$2 x (x^{2}) - 8 x^{2} + 8 x$

Step 1.2

Factor $2 x$ out of $- 8 x^{2}$ .

$2 x (x^{2}) + 2 x (- 4 x) + 8 x$

Step 1.3

Factor $2 x$ out of $8 x$ .

$2 x (x^{2}) + 2 x (- 4 x) + 2 x (4)$

Step 1.4

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

$2 x (x^{2} - 4 x) + 2 x (4)$

Step 1.5

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

$2 x (x^{2} - 4 x + 4)$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

$2 x (x^{2} - 4 x + 2^{2})$

Step 2.2

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

$4 x = 2 \cdot x \cdot 2$

Step 2.3

Rewrite the polynomial.

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

Step 2.4

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

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