Factor 4x^2-5xy-6y^2

$4 x^{2} - 5 x y - 6 y^{2}$

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 $a \cdot c = 4 \cdot - 6 = - 24$ and whose sum is $b = - 5$ .

Reorder terms.

$4 x^{2} - 6 y^{2} - 5 x y$

Reorder $- 6 y^{2}$ and $- 5 x y$ .

$4 x^{2} - 5 x y - 6 y^{2}$

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

$4 x^{2} - 5 (x y) - 6 y^{2}$

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

$4 x^{2} + (3 - 8) (x y) - 6 y^{2}$

Apply the distributive property.

$4 x^{2} + 3 (x y) - 8 (x y) - 6 y^{2}$

Remove unnecessary parentheses.

$4 x^{2} + 3 x y - 8 (x y) - 6 y^{2}$

Remove unnecessary parentheses.

$4 x^{2} + 3 x y - 8 x y - 6 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} + 3 x y) - 8 x y - 6 y^{2}$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 3 y$ .

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

Factor 4x^2-5xy-6y^2

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