Factor 3x^2+5x+2

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

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

Factor $5$ out of $5 x$ .

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

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Factor the polynomial by factoring out the greatest common factor, $3 x + 2$ .

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

Factor 3x^2+5x+2

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