Factor 3a^2+8a+5

$3 a^{2} + 8 a + 5$

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 $a \cdot c = 3 \cdot 5 = 15$ and whose sum is $b = 8$ .

Factor $8$ out of $8 a$ .

$3 a^{2} + 8 (a) + 5$

Rewrite $8$ as $3$ plus $5$

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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

Factor 3a^2+8a+5

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