Factor 16x^2+16x+3

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

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

Factor $16$ out of $16 x$ .

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$4 x (4 x + 1) + 3 (4 x + 1)$

Step 3

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

$(4 x + 1) (4 x + 3)$

Factor 16x^2+16x+3

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