Factor v^5+7v^4-4v^3-28v^2

$v^{5} + 7 v^{4} - 4 v^{3} - 28 v^{2}$

Step 1

Factor $v^{2}$ out of $v^{5} + 7 v^{4} - 4 v^{3} - 28 v^{2}$ .

Factor $v^{2}$ out of $v^{5}$ .

$v^{2} v^{3} + 7 v^{4} - 4 v^{3} - 28 v^{2}$

Factor $v^{2}$ out of $7 v^{4}$ .

$v^{2} v^{3} + v^{2} (7 v^{2}) - 4 v^{3} - 28 v^{2}$

Factor $v^{2}$ out of $- 4 v^{3}$ .

$v^{2} v^{3} + v^{2} (7 v^{2}) + v^{2} (- 4 v) - 28 v^{2}$

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

$v^{2} v^{3} + v^{2} (7 v^{2}) + v^{2} (- 4 v) + v^{2} \cdot - 28$

Factor $v^{2}$ out of $v^{2} v^{3} + v^{2} (7 v^{2})$ .

$v^{2} (v^{3} + 7 v^{2}) + v^{2} (- 4 v) + v^{2} \cdot - 28$

Factor $v^{2}$ out of $v^{2} (v^{3} + 7 v^{2}) + v^{2} (- 4 v)$ .

$v^{2} (v^{3} + 7 v^{2} - 4 v) + v^{2} \cdot - 28$

Factor $v^{2}$ out of $v^{2} (v^{3} + 7 v^{2} - 4 v) + v^{2} \cdot - 28$ .

$v^{2} (v^{3} + 7 v^{2} - 4 v - 28)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$v^{2} ((v^{3} + 7 v^{2}) - 4 v - 28)$

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

$v^{2} (v^{2} (v + 7) - 4 (v + 7))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $v + 7$ .

$v^{2} ((v + 7) (v^{2} - 4))$

Step 4

Rewrite $4$ as $2^{2}$ .

$v^{2} ((v + 7) (v^{2} - 2^{2}))$

Step 5

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = v$ and $b = 2$ .

$v^{2} ((v + 7) ((v + 2) (v - 2)))$

Remove unnecessary parentheses.

$v^{2} ((v + 7) (v + 2) (v - 2))$

Remove unnecessary parentheses.

$v^{2} (v + 7) (v + 2) (v - 2)$