Factor 4x^2+8x+3

$4 x^{2} + 8 x + 3$

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 $a \cdot c = 4 \cdot 3 = 12$ and whose sum is $b = 8$ .

Factor $8$ out of $8 x$ .

$4 x^{2} + 8 (x) + 3$

Rewrite $8$ as $2$ plus $6$

$4 x^{2} + (2 + 6) x + 3$

Apply the distributive property.

$4 x^{2} + 2 x + 6 x + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} + 2 x) + 6 x + 3$

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

$2 x (2 x + 1) + 3 (2 x + 1)$

Step 3

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

$(2 x + 1) (2 x + 3)$

Factor 4x^2+8x+3

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