Factor 6a^2-28a+16

$6 a^{2} - 28 a + 16$

Step 1

Factor $2$ out of $6 a^{2} - 28 a + 16$ .

Factor $2$ out of $6 a^{2}$ .

$2 (3 a^{2}) - 28 a + 16$

Factor $2$ out of $- 28 a$ .

$2 (3 a^{2}) + 2 (- 14 a) + 16$

Factor $2$ out of $16$ .

$2 (3 a^{2}) + 2 (- 14 a) + 2 (8)$

Factor $2$ out of $2 (3 a^{2}) + 2 (- 14 a)$ .

$2 (3 a^{2} - 14 a) + 2 (8)$

Factor $2$ out of $2 (3 a^{2} - 14 a) + 2 (8)$ .

$2 (3 a^{2} - 14 a + 8)$

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 3 \cdot 8 = 24$ and whose sum is $b = - 14$ .

Factor $- 14$ out of $- 14 a$ .

$2 (3 a^{2} - 14 (a) + 8)$

Rewrite $- 14$ as $- 2$ plus $- 12$

$2 (3 a^{2} + (- 2 - 12) a + 8)$

Apply the distributive property.

$2 (3 a^{2} - 2 a - 12 a + 8)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((3 a^{2} - 2 a) - 12 a + 8)$

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

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

Factor the polynomial by factoring out the greatest common factor, $3 a - 2$ .

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

Remove unnecessary parentheses.

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

Factor 6a^2-28a+16

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