Factor 2n^2+5n+2

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

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 $a \cdot c = 2 \cdot 2 = 4$ and whose sum is $b = 5$ .

Factor $5$ out of $5 n$ .

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

Rewrite $5$ as $1$ plus $4$

$2 n^{2} + (1 + 4) n + 2$

Apply the distributive property.

$2 n^{2} + 1 n + 4 n + 2$

Multiply $n$ by $1$ .

$2 n^{2} + n + 4 n + 2$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 n^{2} + n) + 4 n + 2$

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

$n (2 n + 1) + 2 (2 n + 1)$

Step 3

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

$(2 n + 1) (n + 2)$

Factor 2n^2+5n+2

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