Factor 2x^2+11x+15

$2 x^{2} + 11 x + 15$

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 $b = 11$ .

Factor $11$ out of $11 x$ .

$2 x^{2} + 11 (x) + 15$

Rewrite $11$ as $5$ plus $6$

$2 x^{2} + (5 + 6) x + 15$

Apply the distributive property.

$2 x^{2} + 5 x + 6 x + 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 5 x) + 6 x + 15$

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

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

Step 3

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

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

Factor 2x^2+11x+15

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