Algebra Examples

6 x^{2} - 6 x - 36

$6 x^{2} - 6 x - 36$

Step 1

Factor

6

$6$ out of

6 x^{2} - 6 x - 36

$6 x^{2} - 6 x - 36$ .

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Step 1.1

Factor

6

$6$ out of

6 x^{2}

$6 x^{2}$ .

6 (x^{2}) - 6 x - 36

$6 (x^{2}) - 6 x - 36$

Step 1.2

Factor

6

$6$ out of

- 6 x

$- 6 x$ .

6 (x^{2}) + 6 (- x) - 36

$6 (x^{2}) + 6 (- x) - 36$

Step 1.3

Factor

6

$6$ out of

- 36

$- 36$ .

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

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

Step 1.4

Factor

6

$6$ out of

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

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

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

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

Step 1.5

Factor

6

$6$ out of

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

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

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

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

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

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

Step 2

Factor.

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Step 2.1

Factor

x^{2} - x - 6

$x^{2} - x - 6$ using the AC method.

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Step 2.1.1

Consider the form

x^{2} + b x + c

$x^{2} + b x + c$ . Find a pair of integers whose product is

c

$c$ and whose sum is

b

$b$ . In this case, whose product is

- 6

$- 6$ and whose sum is

- 1

$- 1$ .

- 3, 2

$- 3, 2$

Step 2.1.2

Write the factored form using these integers.

6 ((x - 3) (x + 2))

$6 ((x - 3) (x + 2))$

6 ((x - 3) (x + 2))

$6 ((x - 3) (x + 2))$

Step 2.2

Remove unnecessary parentheses.

6 (x - 3) (x + 2)

$6 (x - 3) (x + 2)$

6 (x - 3) (x + 2)

$6 (x - 3) (x + 2)$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$