Factor 4x^2+13x+3

$4 x^{2} + 13 x + 3$

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 $b = 13$ .

Factor $13$ out of $13 x$ .

$4 x^{2} + 13 (x) + 3$

Rewrite $13$ as $1$ plus $12$

$4 x^{2} + (1 + 12) x + 3$

Apply the distributive property.

$4 x^{2} + 1 x + 12 x + 3$

Multiply $x$ by $1$ .

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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

Factor 4x^2+13x+3

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