Factor 2x^2+5x+3

$2 x^{2} + 5 x + 3$

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 $5 x$ .

$2 x^{2} + 5 (x) + 3$

Rewrite $5$ as $2$ plus $3$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 x (x + 1) + 3 (x + 1)$

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

$(x + 1) (2 x + 3)$

Factor 2x^2+5x+3

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