Factor 2n^2+5n-3

$2 n^{2} + 5 n - 3$

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 $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = 5$ .

Factor $5$ out of $5 n$ .

$2 n^{2} + 5 (n) - 3$

Rewrite $5$ as $- 1$ plus $6$

$2 n^{2} + (- 1 + 6) n - 3$

Apply the distributive property.

$2 n^{2} - 1 n + 6 n - 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 n^{2} - 1 n) + 6 n - 3$

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

$n (2 n - 1) + 3 (2 n - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 n - 1$ .

$(2 n - 1) (n + 3)$

Factor 2n^2+5n-3

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