Factor 7y^2-13y-2

$7 y^{2} - 13 y - 2$

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 $a \cdot c = 7 \cdot - 2 = - 14$ and whose sum is $b = - 13$ .

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

$7 y^{2} - 13 (y) - 2$

Rewrite $- 13$ as $1$ plus $- 14$

$7 y^{2} + (1 - 14) y - 2$

Apply the distributive property.

$7 y^{2} + 1 y - 14 y - 2$

Multiply $y$ by $1$ .

$7 y^{2} + y - 14 y - 2$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 y^{2} + y) - 14 y - 2$

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

$y (7 y + 1) - 2 (7 y + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 y + 1$ .

$(7 y + 1) (y - 2)$

Factor 7y^2-13y-2

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