Algebra Examples

$3 x^{2} - 3 x - 18$

Step 1

Factor $3$ out of $3 x^{2} - 3 x - 18$ .

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Step 1.1

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

$3 (x^{2}) - 3 x - 18$

Step 1.2

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

$3 (x^{2}) + 3 (- x) - 18$

Step 1.3

Factor $3$ out of $- 18$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Factor.

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Step 2.1

Factor $x^{2} - x - 6$ 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 $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Step 2.1.2

Write the factored form using these integers.

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

Step 2.2

Remove unnecessary parentheses.

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