Calculus Examples

$12 x^{2} - 48 x + 36$

Step 1

Factor $12$ out of $12 x^{2} - 48 x + 36$ .

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Step 1.1

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

$12 (x^{2}) - 48 x + 36$

Step 1.2

Factor $12$ out of $- 48 x$ .

$12 (x^{2}) + 12 (- 4 x) + 36$

Step 1.3

Factor $12$ out of $36$ .

$12 x^{2} + 12 (- 4 x) + 12 \cdot 3$

Step 1.4

Factor $12$ out of $12 x^{2} + 12 (- 4 x)$ .

$12 (x^{2} - 4 x) + 12 \cdot 3$

Step 1.5

Factor $12$ out of $12 (x^{2} - 4 x) + 12 \cdot 3$ .

$12 (x^{2} - 4 x + 3)$

Step 2

Factor.

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Step 2.1

Factor $x^{2} - 4 x + 3$ using the AC method.

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Step 2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $3$ and whose sum is $- 4$ .

$- 3, - 1$

Step 2.1.2

Write the factored form using these integers.

$12 ((x - 3) (x - 1))$

Step 2.2

Remove unnecessary parentheses.

$12 (x - 3) (x - 1)$