Factor 8v^2-30v+18

$8 v^{2} - 30 v + 18$

Step 1

Factor $2$ out of $8 v^{2} - 30 v + 18$ .

Factor $2$ out of $8 v^{2}$ .

$2 (4 v^{2}) - 30 v + 18$

Factor $2$ out of $- 30 v$ .

$2 (4 v^{2}) + 2 (- 15 v) + 18$

Factor $2$ out of $18$ .

$2 (4 v^{2}) + 2 (- 15 v) + 2 (9)$

Factor $2$ out of $2 (4 v^{2}) + 2 (- 15 v)$ .

$2 (4 v^{2} - 15 v) + 2 (9)$

Factor $2$ out of $2 (4 v^{2} - 15 v) + 2 (9)$ .

$2 (4 v^{2} - 15 v + 9)$

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 $a \cdot c = 4 \cdot 9 = 36$ and whose sum is $b = - 15$ .

Factor $- 15$ out of $- 15 v$ .

$2 (4 v^{2} - 15 (v) + 9)$

Rewrite $- 15$ as $- 3$ plus $- 12$

$2 (4 v^{2} + (- 3 - 12) v + 9)$

Apply the distributive property.

$2 (4 v^{2} - 3 v - 12 v + 9)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((4 v^{2} - 3 v) - 12 v + 9)$

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

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

Factor the polynomial by factoring out the greatest common factor, $4 v - 3$ .

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

Remove unnecessary parentheses.

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

Factor 8v^2-30v+18

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