Algebra Examples

$105 n^{3} + 175 n^{2} - 75 n - 125$

Step 1

Factor $5$ out of $105 n^{3} + 175 n^{2} - 75 n - 125$ .

Tap for more steps...

Step 1.1

Factor $5$ out of $105 n^{3}$ .

$5 (21 n^{3}) + 175 n^{2} - 75 n - 125$

Step 1.2

Factor $5$ out of $175 n^{2}$ .

$5 (21 n^{3}) + 5 (35 n^{2}) - 75 n - 125$

Step 1.3

Factor $5$ out of $- 75 n$ .

$5 (21 n^{3}) + 5 (35 n^{2}) + 5 (- 15 n) - 125$

Step 1.4

Factor $5$ out of $- 125$ .

$5 (21 n^{3}) + 5 (35 n^{2}) + 5 (- 15 n) + 5 (- 25)$

Step 1.5

Factor $5$ out of $5 (21 n^{3}) + 5 (35 n^{2})$ .

$5 (21 n^{3} + 35 n^{2}) + 5 (- 15 n) + 5 (- 25)$

Step 1.6

Factor $5$ out of $5 (21 n^{3} + 35 n^{2}) + 5 (- 15 n)$ .

$5 (21 n^{3} + 35 n^{2} - 15 n) + 5 (- 25)$

Step 1.7

Factor $5$ out of $5 (21 n^{3} + 35 n^{2} - 15 n) + 5 (- 25)$ .

$5 (21 n^{3} + 35 n^{2} - 15 n - 25)$

Step 2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.1

Group the first two terms and the last two terms.

$5 ((21 n^{3} + 35 n^{2}) - 15 n - 25)$

Step 2.2

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

$5 (7 n^{2} (3 n + 5) - 5 (3 n + 5))$

Step 3

Factor.

Tap for more steps...

Step 3.1

Factor the polynomial by factoring out the greatest common factor, $3 n + 5$ .

$5 ((3 n + 5) (7 n^{2} - 5))$

Step 3.2

Remove unnecessary parentheses.

$5 (3 n + 5) (7 n^{2} - 5)$