Factor -2c^4-2c^3+2c^2+2c

$- 2 c^{4} - 2 c^{3} + 2 c^{2} + 2 c$

Step 1

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

Factor $2 c$ out of $- 2 c^{4}$ .

$2 c (- c^{3}) - 2 c^{3} + 2 c^{2} + 2 c$

Factor $2 c$ out of $- 2 c^{3}$ .

$2 c (- c^{3}) + 2 c (- c^{2}) + 2 c^{2} + 2 c$

Factor $2 c$ out of $2 c^{2}$ .

$2 c (- c^{3}) + 2 c (- c^{2}) + 2 c (c) + 2 c$

Factor $2 c$ out of $2 c$ .

$2 c (- c^{3}) + 2 c (- c^{2}) + 2 c (c) + 2 c (1)$

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

$2 c (- c^{3} - c^{2}) + 2 c (c) + 2 c (1)$

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

$2 c (- c^{3} - c^{2} + c) + 2 c (1)$

Factor $2 c$ out of $2 c (- c^{3} - c^{2} + c) + 2 c (1)$ .

$2 c (- c^{3} - c^{2} + c + 1)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 c ((- c^{3} - c^{2}) + c + 1)$

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

$2 c (c^{2} (- c - 1) - 1 (- c - 1))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $- c - 1$ .

$2 c ((- c - 1) (c^{2} - 1))$

Step 4

Rewrite $1$ as $1^{2}$ .

$2 c ((- c - 1) (c^{2} - 1^{2}))$

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 $a = c$ and $b = 1$ .

$2 c ((- c - 1) ((c + 1) (c - 1)))$

Remove unnecessary parentheses.

$2 c ((- c - 1) (c + 1) (c - 1))$

Step 6

Factor.

Combine exponents.

Factor $- 1$ out of $- c$ .

$2 c ((- (c) - 1) (c + 1) (c - 1))$

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

$2 c ((- (c) - 1 (1)) (c + 1) (c - 1))$

Factor $- 1$ out of $- (c) - 1 (1)$ .

$2 c (- (c + 1) (c + 1) (c - 1))$

Rewrite $- (c + 1)$ as $- 1 (c + 1)$ .

$2 c (- 1 (c + 1) (c + 1) (c - 1))$

Raise $c + 1$ to the power of $1$ .

$2 c (- 1 ({(c + 1)}^{1} (c + 1)) (c - 1))$

Raise $c + 1$ to the power of $1$ .

$2 c (- 1 ({(c + 1)}^{1} {(c + 1)}^{1}) (c - 1))$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 c (- 1 {(c + 1)}^{1 + 1} (c - 1))$

Add $1$ and $1$ .

$2 c (- 1 {(c + 1)}^{2} (c - 1))$

Remove unnecessary parentheses.

$2 c \cdot - 1 {(c + 1)}^{2} (c - 1)$

Step 7

Combine exponents.

Factor out negative.

$- (2 c {(c + 1)}^{2} (c - 1))$

Multiply $2$ by $- 1$ .

$- 2 (c {(c + 1)}^{2} (c - 1))$

Step 8

Remove unnecessary parentheses.

$- 2 c {(c + 1)}^{2} (c - 1)$

Factor -2c^4-2c^3+2c^2+2c

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