Factor 3x^2+11xy-20y^2

$3 x^{2} + 11 x y - 20 y^{2}$

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 $a \cdot c = 3 \cdot - 20 = - 60$ and whose sum is $b = 11$ .

Reorder terms.

$3 x^{2} - 20 y^{2} + 11 x y$

Reorder $- 20 y^{2}$ and $11 x y$ .

$3 x^{2} + 11 x y - 20 y^{2}$

Factor $11$ out of $11 x y$ .

$3 x^{2} + 11 (x y) - 20 y^{2}$

Rewrite $11$ as $- 4$ plus $15$

$3 x^{2} + (- 4 + 15) (x y) - 20 y^{2}$

Apply the distributive property.

$3 x^{2} - 4 (x y) + 15 (x y) - 20 y^{2}$

Remove unnecessary parentheses.

$3 x^{2} - 4 x y + 15 (x y) - 20 y^{2}$

Remove unnecessary parentheses.

$3 x^{2} - 4 x y + 15 x y - 20 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} - 4 x y) + 15 x y - 20 y^{2}$

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

$x (3 x - 4 y) + 5 y (3 x - 4 y)$

Step 3

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

$(3 x - 4 y) (x + 5 y)$

Factor 3x^2+11xy-20y^2

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