Factor 2x^2+5xy-12y^2

$2 x^{2} + 5 x y - 12 y^{2}$

Step 1

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 $a \cdot c = 2 \cdot - 12 = - 24$ and whose sum is $b = 5$ .

Reorder terms.

$2 x^{2} - 12 y^{2} + 5 x y$

Reorder $- 12 y^{2}$ and $5 x y$ .

$2 x^{2} + 5 x y - 12 y^{2}$

Factor $5$ out of $5 x y$ .

$2 x^{2} + 5 (x y) - 12 y^{2}$

Rewrite $5$ as $- 3$ plus $8$

$2 x^{2} + (- 3 + 8) (x y) - 12 y^{2}$

Apply the distributive property.

$2 x^{2} - 3 (x y) + 8 (x y) - 12 y^{2}$

Remove unnecessary parentheses.

$2 x^{2} - 3 x y + 8 (x y) - 12 y^{2}$

Remove unnecessary parentheses.

$2 x^{2} - 3 x y + 8 x y - 12 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 3 x y) + 8 x y - 12 y^{2}$

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

$x (2 x - 3 y) + 4 y (2 x - 3 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x - 3 y$ .

$(2 x - 3 y) (x + 4 y)$

Factor 2x^2+5xy-12y^2

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