Factor -30x^3-2x^2y+4xy^2

$- 30 x^{3} - 2 x^{2} y + 4 x y^{2}$

Factor $- 2 x$ out of $- 30 x^{3} - 2 x^{2} y + 4 x y^{2}$ .

Reorder the expression.

Move $- 30 x^{3}$ .

$- 2 x^{2} y + 4 x y^{2} - 30 x^{3}$

Reorder $- 2 x^{2} y$ and $4 x y^{2}$ .

$4 x y^{2} - 2 x^{2} y - 30 x^{3}$

Factor $- 2 x$ out of $4 x y^{2}$ .

$- 2 x (- 2 y^{2}) - 2 x^{2} y - 30 x^{3}$

Factor $- 2 x$ out of $- 2 x^{2} y$ .

$- 2 x (- 2 y^{2}) - 2 x (x y) - 30 x^{3}$

Factor $- 2 x$ out of $- 30 x^{3}$ .

$- 2 x (- 2 y^{2}) - 2 x (x y) - 2 x (15 x^{2})$

Factor $- 2 x$ out of $- 2 x (- 2 y^{2}) - 2 x (x y)$ .

$- 2 x (- 2 y^{2} + x y) - 2 x (15 x^{2})$

Factor $- 2 x$ out of $- 2 x (- 2 y^{2} + x y) - 2 x (15 x^{2})$ .

$- 2 x (- 2 y^{2} + x y + 15 x^{2})$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 15 \cdot - 2 = - 30$ and whose sum is $b = 1$ .

Reorder terms.

$- 2 x (15 x^{2} - 2 y^{2} + x y)$

Reorder $- 2 y^{2}$ and $x y$ .

$- 2 x (15 x^{2} + x y - 2 y^{2})$

Factor $1$ out of $x y$ .

$- 2 x (15 x^{2} + 1 (x y) - 2 y^{2})$

Rewrite $1$ as $- 5$ plus $6$

$- 2 x (15 x^{2} + (- 5 + 6) (x y) - 2 y^{2})$

Apply the distributive property.

$- 2 x (15 x^{2} - 5 (x y) + 6 (x y) - 2 y^{2})$

Remove unnecessary parentheses.

$- 2 x (15 x^{2} - 5 x y + 6 (x y) - 2 y^{2})$

Remove unnecessary parentheses.

$- 2 x (15 x^{2} - 5 x y + 6 x y - 2 y^{2})$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- 2 x ((15 x^{2} - 5 x y) + 6 x y - 2 y^{2})$

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

$- 2 x (5 x (3 x - 1 y) + 2 y (3 x - y))$

Factor the polynomial by factoring out the greatest common factor, $3 x - 1 y$ .

$- 2 x ((3 x - 1 y) (5 x + 2 y))$

Factor.

Rewrite $- 1 y$ as $- y$ .

$- 2 x ((3 x - y) (5 x + 2 y))$

Remove unnecessary parentheses.

$- 2 x (3 x - y) (5 x + 2 y)$

Factor -30x^3-2x^2y+4xy^2

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