Factor 9r^2+15r+6

$9 r^{2} + 15 r + 6$

Step 1

Factor $3$ out of $9 r^{2} + 15 r + 6$ .

Factor $3$ out of $9 r^{2}$ .

$3 (3 r^{2}) + 15 r + 6$

Factor $3$ out of $15 r$ .

$3 (3 r^{2}) + 3 (5 r) + 6$

Factor $3$ out of $6$ .

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

Factor $3$ out of $3 (3 r^{2}) + 3 (5 r)$ .

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

Factor $3$ out of $3 (3 r^{2} + 5 r) + 3 (2)$ .

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

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 3 \cdot 2 = 6$ and whose sum is $b = 5$ .

Factor $5$ out of $5 r$ .

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

Rewrite $5$ as $2$ plus $3$

$3 (3 r^{2} + (2 + 3) r + 2)$

Apply the distributive property.

$3 (3 r^{2} + 2 r + 3 r + 2)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((3 r^{2} + 2 r) + 3 r + 2)$

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

$3 (r (3 r + 2) + 1 (3 r + 2))$

Factor the polynomial by factoring out the greatest common factor, $3 r + 2$ .

$3 ((3 r + 2) (r + 1))$

Remove unnecessary parentheses.

$3 (3 r + 2) (r + 1)$

Factor 9r^2+15r+6

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