Pre-Algebra Examples

$6 a^{2} + 24 a - 12 a - 48$

Step 1

Factor out the GCF of $6$ from $6 a^{2} + 24 a - 12 a - 48$ .

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Step 1.1

Factor out the GCF of $6$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $6$ from the expression $6 a^{2}$ .

$6 (a^{2}) + 24 a - 12 a - 48$

Step 1.1.2

Factor out the GCF of $6$ from the expression $24 a$ .

$6 (a^{2}) + 6 (4 a) - 12 a - 48$

Step 1.1.3

Factor out the GCF of $6$ from the expression $- 12 a$ .

$6 (a^{2}) + 6 (4 a) + 6 (- 2 a) - 48$

Step 1.1.4

Factor out the GCF of $6$ from the expression $- 48$ .

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

Step 1.2

Since all the terms share a common factor of $6$ , it can be factored out of each term.

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

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

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

Step 2.2

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

$6 (a (a + 4) - 2 (a + 4))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $a + 4$ .

$6 ((a + 4) (a - 2))$