Factor 5t^6+2t^5-5t^4-2t^3

$5 t^{6} + 2 t^{5} - 5 t^{4} - 2 t^{3}$

Step 1

Factor $t^{3}$ out of $5 t^{6} + 2 t^{5} - 5 t^{4} - 2 t^{3}$ .

Factor $t^{3}$ out of $5 t^{6}$ .

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

Factor $t^{3}$ out of $2 t^{5}$ .

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

Factor $t^{3}$ out of $- 5 t^{4}$ .

$t^{3} (5 t^{3}) + t^{3} (2 t^{2}) + t^{3} (- 5 t) - 2 t^{3}$

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

$t^{3} (5 t^{3}) + t^{3} (2 t^{2}) + t^{3} (- 5 t) + t^{3} \cdot - 2$

Factor $t^{3}$ out of $t^{3} (5 t^{3}) + t^{3} (2 t^{2})$ .

$t^{3} (5 t^{3} + 2 t^{2}) + t^{3} (- 5 t) + t^{3} \cdot - 2$

Factor $t^{3}$ out of $t^{3} (5 t^{3} + 2 t^{2}) + t^{3} (- 5 t)$ .

$t^{3} (5 t^{3} + 2 t^{2} - 5 t) + t^{3} \cdot - 2$

Factor $t^{3}$ out of $t^{3} (5 t^{3} + 2 t^{2} - 5 t) + t^{3} \cdot - 2$ .

$t^{3} (5 t^{3} + 2 t^{2} - 5 t - 2)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$t^{3} ((5 t^{3} + 2 t^{2}) - 5 t - 2)$

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

$t^{3} (t^{2} (5 t + 2) - (5 t + 2))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 t + 2$ .

$t^{3} ((5 t + 2) (t^{2} - 1))$

Step 4

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

$t^{3} ((5 t + 2) (t^{2} - 1^{2}))$

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 $a = t$ and $b = 1$ .

$t^{3} ((5 t + 2) ((t + 1) (t - 1)))$

Remove unnecessary parentheses.

$t^{3} ((5 t + 2) (t + 1) (t - 1))$

Remove unnecessary parentheses.

$t^{3} (5 t + 2) (t + 1) (t - 1)$