Factor 2n^2-11n+15

$2 n^{2} - 11 n + 15$

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 $- 11 n$ .

$2 n^{2} - 11 (n) + 15$

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

$2 n^{2} + (- 5 - 6) n + 15$

Apply the distributive property.

$2 n^{2} - 5 n - 6 n + 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 n^{2} - 5 n) - 6 n + 15$

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

$n (2 n - 5) - 3 (2 n - 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 n - 5$ .

$(2 n - 5) (n - 3)$

Factor 2n^2-11n+15

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