Factor 3x^2-7xy-6y^2

$3 x^{2} - 7 x y - 6 y^{2}$

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 $a \cdot c = 3 \cdot - 6 = - 18$ and whose sum is $b = - 7$ .

Reorder terms.

$3 x^{2} - 6 y^{2} - 7 x y$

Reorder $- 6 y^{2}$ and $- 7 x y$ .

$3 x^{2} - 7 x y - 6 y^{2}$

Factor $- 7$ out of $- 7 x y$ .

$3 x^{2} - 7 (x y) - 6 y^{2}$

Rewrite $- 7$ as $2$ plus $- 9$

$3 x^{2} + (2 - 9) (x y) - 6 y^{2}$

Apply the distributive property.

$3 x^{2} + 2 (x y) - 9 (x y) - 6 y^{2}$

Remove unnecessary parentheses.

$3 x^{2} + 2 x y - 9 (x y) - 6 y^{2}$

Remove unnecessary parentheses.

$3 x^{2} + 2 x y - 9 x y - 6 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} + 2 x y) - 9 x y - 6 y^{2}$

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

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

Step 3

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

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

Factor 3x^2-7xy-6y^2

Related Questions

Support LCMGCF.com by disabling your adblocker.