Factor 3y^2+16y+16

$3 y^{2} + 16 y + 16$

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 $a \cdot c = 3 \cdot 16 = 48$ and whose sum is $b = 16$ .

Factor $16$ out of $16 y$ .

$3 y^{2} + 16 (y) + 16$

Rewrite $16$ as $4$ plus $12$

$3 y^{2} + (4 + 12) y + 16$

Apply the distributive property.

$3 y^{2} + 4 y + 12 y + 16$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 y^{2} + 4 y) + 12 y + 16$

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

$y (3 y + 4) + 4 (3 y + 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 y + 4$ .

$(3 y + 4) (y + 4)$

Factor 3y^2+16y+16

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