Factor 3x^2+xy-10y^2

$3 x^{2} + x y - 10 y^{2}$

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 $a \cdot c = 3 \cdot - 10 = - 30$ and whose sum is $b = 1$ .

Reorder terms.

$3 x^{2} - 10 y^{2} + x y$

Reorder $- 10 y^{2}$ and $x y$ .

$3 x^{2} + x y - 10 y^{2}$

Factor $1$ out of $x y$ .

$3 x^{2} + 1 (x y) - 10 y^{2}$

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

$3 x^{2} + (- 5 + 6) (x y) - 10 y^{2}$

Apply the distributive property.

$3 x^{2} - 5 (x y) + 6 (x y) - 10 y^{2}$

Remove unnecessary parentheses.

$3 x^{2} - 5 x y + 6 (x y) - 10 y^{2}$

Remove unnecessary parentheses.

$3 x^{2} - 5 x y + 6 x y - 10 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} - 5 x y) + 6 x y - 10 y^{2}$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x - 5 y$ .

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

Factor 3x^2+xy-10y^2

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