Calculus Examples

$- 3 x^{2} + 6 x - 3$

Step 1

Factor $- 3$ out of $- 3 x^{2} + 6 x - 3$ .

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Step 1.1

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

$- 3 (x^{2}) + 6 x - 3$

Step 1.2

Factor $- 3$ out of $6 x$ .

$- 3 (x^{2}) - 3 (- 2 x) - 3$

Step 1.3

Factor $- 3$ out of $- 3$ .

$- 3 (x^{2}) - 3 (- 2 x) - 3 (1)$

Step 1.4

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

$- 3 (x^{2} - 2 x) - 3 (1)$

Step 1.5

Factor $- 3$ out of $- 3 (x^{2} - 2 x) - 3 (1)$ .

$- 3 (x^{2} - 2 x + 1)$

Step 2

Factor using the perfect square rule.

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Step 2.1

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

$- 3 (x^{2} - 2 x + 1^{2})$

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.

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

Step 2.3

Rewrite the polynomial.

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

Step 2.4

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

$- 3 {(x - 1)}^{2}$