Factor 10x^2-19xy+6y^2

$10 x^{2} - 19 x y + 6 y^{2}$

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 $a \cdot c = 10 \cdot 6 = 60$ and whose sum is $b = - 19$ .

Reorder terms.

$10 x^{2} + 6 y^{2} - 19 x y$

Reorder $6 y^{2}$ and $- 19 x y$ .

$10 x^{2} - 19 x y + 6 y^{2}$

Factor $- 19$ out of $- 19 x y$ .

$10 x^{2} - 19 (x y) + 6 y^{2}$

Rewrite $- 19$ as $- 4$ plus $- 15$

$10 x^{2} + (- 4 - 15) (x y) + 6 y^{2}$

Apply the distributive property.

$10 x^{2} - 4 (x y) - 15 (x y) + 6 y^{2}$

Remove unnecessary parentheses.

$10 x^{2} - 4 x y - 15 (x y) + 6 y^{2}$

Remove unnecessary parentheses.

$10 x^{2} - 4 x y - 15 x y + 6 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 x^{2} - 4 x y) - 15 x y + 6 y^{2}$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 2 y$ .

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

Factor 10x^2-19xy+6y^2

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