Factor -z^6-2z^5-16z^4-32z^3

$- z^{6} - 2 z^{5} - 16 z^{4} - 32 z^{3}$

Step 1

Factor $z^{3}$ out of $- z^{6} - 2 z^{5} - 16 z^{4} - 32 z^{3}$ .

Factor $z^{3}$ out of $- z^{6}$ .

$z^{3} (- z^{3}) - 2 z^{5} - 16 z^{4} - 32 z^{3}$

Factor $z^{3}$ out of $- 2 z^{5}$ .

$z^{3} (- z^{3}) + z^{3} (- 2 z^{2}) - 16 z^{4} - 32 z^{3}$

Factor $z^{3}$ out of $- 16 z^{4}$ .

$z^{3} (- z^{3}) + z^{3} (- 2 z^{2}) + z^{3} (- 16 z) - 32 z^{3}$

Factor $z^{3}$ out of $- 32 z^{3}$ .

$z^{3} (- z^{3}) + z^{3} (- 2 z^{2}) + z^{3} (- 16 z) + z^{3} \cdot - 32$

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

$z^{3} (- z^{3} - 2 z^{2}) + z^{3} (- 16 z) + z^{3} \cdot - 32$

Factor $z^{3}$ out of $z^{3} (- z^{3} - 2 z^{2}) + z^{3} (- 16 z)$ .

$z^{3} (- z^{3} - 2 z^{2} - 16 z) + z^{3} \cdot - 32$

Factor $z^{3}$ out of $z^{3} (- z^{3} - 2 z^{2} - 16 z) + z^{3} \cdot - 32$ .

$z^{3} (- z^{3} - 2 z^{2} - 16 z - 32)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$z^{3} ((- z^{3} - 2 z^{2}) - 16 z - 32)$

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

$z^{3} (z^{2} (- z - 2) + 16 (- z - 2))$

Step 3

Factor.

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

$z^{3} ((- z - 2) (z^{2} + 16))$

Remove unnecessary parentheses.

$z^{3} (- z - 2) (z^{2} + 16)$

Step 4

Factor.

Factor $- 1$ out of $- z - 2$ .

Factor $- 1$ out of $- z$ .

$z^{3} (- (z) - 2) (z^{2} + 16)$

Rewrite $- 2$ as $- 1 (2)$ .

$z^{3} (- (z) - 1 (2)) (z^{2} + 16)$

Factor $- 1$ out of $- (z) - 1 (2)$ .

$z^{3} (- (z + 2)) (z^{2} + 16)$

Remove unnecessary parentheses.

$z^{3} \cdot - 1 (z + 2) (z^{2} + 16)$

Step 5

Factor.

Factor out negative.

$- ((z^{3} (z + 2)) (z^{2} + 16))$

Remove unnecessary parentheses.

$- z^{3} (z + 2) (z^{2} + 16)$

Factor -z^6-2z^5-16z^4-32z^3

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