Factor 2x^2+13x+15

$2 x^{2} + 13 x + 15$

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 $a \cdot c = 2 \cdot 15 = 30$ and whose sum is $b = 13$ .

Factor $13$ out of $13 x$ .

$2 x^{2} + 13 (x) + 15$

Rewrite $13$ as $3$ plus $10$

$2 x^{2} + (3 + 10) x + 15$

Apply the distributive property.

$2 x^{2} + 3 x + 10 x + 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 3 x) + 10 x + 15$

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

$x (2 x + 3) + 5 (2 x + 3)$

Step 3

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

$(2 x + 3) (x + 5)$

Factor 2x^2+13x+15

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