Basic Math Examples

$k^{5} + 2 k^{4} - 2 k^{3} - 4 k^{2}$

Step 1

Factor $k^{2}$ out of $k^{5} + 2 k^{4} - 2 k^{3} - 4 k^{2}$ .

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Step 1.1

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

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

Step 1.2

Factor $k^{2}$ out of $2 k^{4}$ .

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

Step 1.3

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

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

Step 1.4

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

$k^{2} k^{3} + k^{2} (2 k^{2}) + k^{2} (- 2 k) + k^{2} \cdot - 4$

Step 1.5

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

$k^{2} (k^{3} + 2 k^{2}) + k^{2} (- 2 k) + k^{2} \cdot - 4$

Step 1.6

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

$k^{2} (k^{3} + 2 k^{2} - 2 k) + k^{2} \cdot - 4$

Step 1.7

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

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

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.

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

Step 2.2

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

$k^{2} (k^{2} (k + 2) - 2 (k + 2))$

Step 3

Factor.

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Step 3.1

Factor the polynomial by factoring out the greatest common factor, $k + 2$ .

$k^{2} ((k + 2) (k^{2} - 2))$

Step 3.2

Remove unnecessary parentheses.

$k^{2} (k + 2) (k^{2} - 2)$