Factor 2x^2+7x+6

$2 x^{2} + 7 x + 6$

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 $a \cdot c = 2 \cdot 6 = 12$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$2 x^{2} + 7 (x) + 6$

Rewrite $7$ as $3$ plus $4$

$2 x^{2} + (3 + 4) x + 6$

Apply the distributive property.

$2 x^{2} + 3 x + 4 x + 6$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 3 x) + 4 x + 6$

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

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

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

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

Factor 2x^2+7x+6

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