Factor 5a^2+16a+3

$5 a^{2} + 16 a + 3$

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 $a \cdot c = 5 \cdot 3 = 15$ and whose sum is $b = 16$ .

Factor $16$ out of $16 a$ .

$5 a^{2} + 16 (a) + 3$

Rewrite $16$ as $1$ plus $15$

$5 a^{2} + (1 + 15) a + 3$

Apply the distributive property.

$5 a^{2} + 1 a + 15 a + 3$

Multiply $a$ by $1$ .

$5 a^{2} + a + 15 a + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 a^{2} + a) + 15 a + 3$

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

$a (5 a + 1) + 3 (5 a + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 a + 1$ .

$(5 a + 1) (a + 3)$

Factor 5a^2+16a+3

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