Factor 2y^2+13y-24

$2 y^{2} + 13 y - 24$

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 $a \cdot c = 2 \cdot - 24 = - 48$ and whose sum is $b = 13$ .

Factor $13$ out of $13 y$ .

$2 y^{2} + 13 (y) - 24$

Rewrite $13$ as $- 3$ plus $16$

$2 y^{2} + (- 3 + 16) y - 24$

Apply the distributive property.

$2 y^{2} - 3 y + 16 y - 24$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 y^{2} - 3 y) + 16 y - 24$

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

$y (2 y - 3) + 8 (2 y - 3)$

Step 3

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

$(2 y - 3) (y + 8)$

Factor 2y^2+13y-24

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