Algebra Examples

$21 k^{3} - 84 k^{2} + 15 k - 60$

Step 1

Factor $3$ out of $21 k^{3} - 84 k^{2} + 15 k - 60$ .

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Step 1.1

Factor $3$ out of $21 k^{3}$ .

$3 (7 k^{3}) - 84 k^{2} + 15 k - 60$

Step 1.2

Factor $3$ out of $- 84 k^{2}$ .

$3 (7 k^{3}) + 3 (- 28 k^{2}) + 15 k - 60$

Step 1.3

Factor $3$ out of $15 k$ .

$3 (7 k^{3}) + 3 (- 28 k^{2}) + 3 (5 k) - 60$

Step 1.4

Factor $3$ out of $- 60$ .

$3 (7 k^{3}) + 3 (- 28 k^{2}) + 3 (5 k) + 3 (- 20)$

Step 1.5

Factor $3$ out of $3 (7 k^{3}) + 3 (- 28 k^{2})$ .

$3 (7 k^{3} - 28 k^{2}) + 3 (5 k) + 3 (- 20)$

Step 1.6

Factor $3$ out of $3 (7 k^{3} - 28 k^{2}) + 3 (5 k)$ .

$3 (7 k^{3} - 28 k^{2} + 5 k) + 3 (- 20)$

Step 1.7

Factor $3$ out of $3 (7 k^{3} - 28 k^{2} + 5 k) + 3 (- 20)$ .

$3 (7 k^{3} - 28 k^{2} + 5 k - 20)$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$3 ((7 k^{3} - 28 k^{2}) + 5 k - 20)$

Step 2.2

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

$3 (7 k^{2} (k - 4) + 5 (k - 4))$

Step 3

Factor.

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Step 3.1

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

$3 ((k - 4) (7 k^{2} + 5))$

Step 3.2

Remove unnecessary parentheses.

$3 (k - 4) (7 k^{2} + 5)$