Factor 8y^2+14y+3

$8 y^{2} + 14 y + 3$

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 $a \cdot c = 8 \cdot 3 = 24$ and whose sum is $b = 14$ .

Factor $14$ out of $14 y$ .

$8 y^{2} + 14 (y) + 3$

Rewrite $14$ as $2$ plus $12$

$8 y^{2} + (2 + 12) y + 3$

Apply the distributive property.

$8 y^{2} + 2 y + 12 y + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 y^{2} + 2 y) + 12 y + 3$

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

$2 y (4 y + 1) + 3 (4 y + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 y + 1$ .

$(4 y + 1) (2 y + 3)$

Factor 8y^2+14y+3

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