Algebra Examples

$9 - 6 a - 24 a^{2}$

Step 1

Factor $- 3$ out of $9 - 6 a - 24 a^{2}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move $9$ .

$- 6 a - 24 a^{2} + 9$

Step 1.1.2

Reorder $- 6 a$ and $- 24 a^{2}$ .

$- 24 a^{2} - 6 a + 9$

Step 1.2

Factor $- 3$ out of $- 24 a^{2}$ .

$- 3 (8 a^{2}) - 6 a + 9$

Step 1.3

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

$- 3 (8 a^{2}) - 3 (2 a) + 9$

Step 1.4

Factor $- 3$ out of $9$ .

$- 3 (8 a^{2}) - 3 (2 a) - 3 (- 3)$

Step 1.5

Factor $- 3$ out of $- 3 (8 a^{2}) - 3 (2 a)$ .

$- 3 (8 a^{2} + 2 a) - 3 (- 3)$

Step 1.6

Factor $- 3$ out of $- 3 (8 a^{2} + 2 a) - 3 (- 3)$ .

$- 3 (8 a^{2} + 2 a - 3)$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 8 \cdot - 3 = - 24$ and whose sum is $b = 2$ .

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Step 2.1.1.1

Factor $2$ out of $2 a$ .

$- 3 (8 a^{2} + 2 (a) - 3)$

Step 2.1.1.2

Rewrite $2$ as $- 4$ plus $6$

$- 3 (8 a^{2} + (- 4 + 6) a - 3)$

Step 2.1.1.3

Apply the distributive property.

$- 3 (8 a^{2} - 4 a + 6 a - 3)$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$- 3 ((8 a^{2} - 4 a) + 6 a - 3)$

Step 2.1.2.2

Factor out the greatest common factor (GCF) from each group.

$- 3 (4 a (2 a - 1) + 3 (2 a - 1))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $2 a - 1$ .

$- 3 ((2 a - 1) (4 a + 3))$

Step 2.2

Remove unnecessary parentheses.

$- 3 (2 a - 1) (4 a + 3)$