Factor 6v^2-28v+16

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

Step 1

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

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

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

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

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

Factor $2$ out of $16$ .

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

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

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

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

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

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 $- 14 v$ .

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

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 (v (3 v - 2) - 4 (3 v - 2))$

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

$2 ((3 v - 2) (v - 4))$

Remove unnecessary parentheses.

$2 (3 v - 2) (v - 4)$

Factor 6v^2-28v+16

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