Factor 3y^2-13y-10

$3 y^{2} - 13 y - 10$

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 $b = - 13$ .

Factor $- 13$ out of $- 13 y$ .

$3 y^{2} - 13 (y) - 10$

Rewrite $- 13$ as $2$ plus $- 15$

$3 y^{2} + (2 - 15) y - 10$

Apply the distributive property.

$3 y^{2} + 2 y - 15 y - 10$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 y^{2} + 2 y) - 15 y - 10$

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

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

Step 3

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

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

Factor 3y^2-13y-10

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