Factor 14y^2+33y+18

$14 y^{2} + 33 y + 18$

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 $a \cdot c = 14 \cdot 18 = 252$ and whose sum is $b = 33$ .

Factor $33$ out of $33 y$ .

$14 y^{2} + 33 (y) + 18$

Rewrite $33$ as $12$ plus $21$

$14 y^{2} + (12 + 21) y + 18$

Apply the distributive property.

$14 y^{2} + 12 y + 21 y + 18$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 y^{2} + 12 y) + 21 y + 18$

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

$2 y (7 y + 6) + 3 (7 y + 6)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 y + 6$ .

$(7 y + 6) (2 y + 3)$

Factor 14y^2+33y+18

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