Factor 2a^2+7a+3

$2 a^{2} + 7 a + 3$

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 $a \cdot c = 2 \cdot 3 = 6$ and whose sum is $b = 7$ .

Factor $7$ out of $7 a$ .

$2 a^{2} + 7 (a) + 3$

Rewrite $7$ as $1$ plus $6$

$2 a^{2} + (1 + 6) a + 3$

Apply the distributive property.

$2 a^{2} + 1 a + 6 a + 3$

Multiply $a$ by $1$ .

$2 a^{2} + a + 6 a + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 a^{2} + a) + 6 a + 3$

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

$a (2 a + 1) + 3 (2 a + 1)$

Step 3

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

$(2 a + 1) (a + 3)$

Factor 2a^2+7a+3

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