Factor 2y^2+7y+3

$2 y^{2} + 7 y + 3$

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 $b = 7$ .

Factor $7$ out of $7 y$ .

$2 y^{2} + 7 (y) + 3$

Rewrite $7$ as $1$ plus $6$

$2 y^{2} + (1 + 6) y + 3$

Apply the distributive property.

$2 y^{2} + 1 y + 6 y + 3$

Multiply $y$ by $1$ .

$2 y^{2} + y + 6 y + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 y^{2} + y) + 6 y + 3$

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

$y (2 y + 1) + 3 (2 y + 1)$

Step 3

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

$(2 y + 1) (y + 3)$

Factor 2y^2+7y+3

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