Factor -10t^5+12t^4+50t^3-60t^2

$- 10 t^{5} + 12 t^{4} + 50 t^{3} - 60 t^{2}$

Step 1

Factor $2 t^{2}$ out of $- 10 t^{5} + 12 t^{4} + 50 t^{3} - 60 t^{2}$ .

Factor $2 t^{2}$ out of $- 10 t^{5}$ .

$2 t^{2} (- 5 t^{3}) + 12 t^{4} + 50 t^{3} - 60 t^{2}$

Factor $2 t^{2}$ out of $12 t^{4}$ .

$2 t^{2} (- 5 t^{3}) + 2 t^{2} (6 t^{2}) + 50 t^{3} - 60 t^{2}$

Factor $2 t^{2}$ out of $50 t^{3}$ .

$2 t^{2} (- 5 t^{3}) + 2 t^{2} (6 t^{2}) + 2 t^{2} (25 t) - 60 t^{2}$

Factor $2 t^{2}$ out of $- 60 t^{2}$ .

$2 t^{2} (- 5 t^{3}) + 2 t^{2} (6 t^{2}) + 2 t^{2} (25 t) + 2 t^{2} (- 30)$

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

$2 t^{2} (- 5 t^{3} + 6 t^{2}) + 2 t^{2} (25 t) + 2 t^{2} (- 30)$

Factor $2 t^{2}$ out of $2 t^{2} (- 5 t^{3} + 6 t^{2}) + 2 t^{2} (25 t)$ .

$2 t^{2} (- 5 t^{3} + 6 t^{2} + 25 t) + 2 t^{2} (- 30)$

Factor $2 t^{2}$ out of $2 t^{2} (- 5 t^{3} + 6 t^{2} + 25 t) + 2 t^{2} (- 30)$ .

$2 t^{2} (- 5 t^{3} + 6 t^{2} + 25 t - 30)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 t^{2} ((- 5 t^{3} + 6 t^{2}) + 25 t - 30)$

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

$2 t^{2} (t^{2} (- 5 t + 6) - 5 (- 5 t + 6))$

Step 3

Factor.

Factor the polynomial by factoring out the greatest common factor, $- 5 t + 6$ .

$2 t^{2} ((- 5 t + 6) (t^{2} - 5))$

Remove unnecessary parentheses.

$2 t^{2} (- 5 t + 6) (t^{2} - 5)$

Step 4

Factor.

Factor $- 1$ out of $- 5 t + 6$ .

Factor $- 1$ out of $- 5 t$ .

$2 t^{2} (- (5 t) + 6) (t^{2} - 5)$

Rewrite $6$ as $- 1 (- 6)$ .

$2 t^{2} (- (5 t) - 1 (- 6)) (t^{2} - 5)$

Factor $- 1$ out of $- (5 t) - 1 (- 6)$ .

$2 t^{2} (- (5 t - 6)) (t^{2} - 5)$

Remove unnecessary parentheses.

$2 t^{2} \cdot - 1 (5 t - 6) (t^{2} - 5)$

Step 5

Factor.

Combine exponents.

Factor out negative.

$- ((2 t^{2} (5 t - 6)) (t^{2} - 5))$

Multiply $2$ by $- 1$ .

$- 2 ((t^{2} (5 t - 6)) (t^{2} - 5))$

Remove unnecessary parentheses.

$- 2 t^{2} (5 t - 6) (t^{2} - 5)$

Factor -10t^5+12t^4+50t^3-60t^2

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