Factor 8x^2+18x+9

$8 x^{2} + 18 x + 9$

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 $a \cdot c = 8 \cdot 9 = 72$ and whose sum is $b = 18$ .

Factor $18$ out of $18 x$ .

$8 x^{2} + 18 (x) + 9$

Rewrite $18$ as $6$ plus $12$

$8 x^{2} + (6 + 12) x + 9$

Apply the distributive property.

$8 x^{2} + 6 x + 12 x + 9$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} + 6 x) + 12 x + 9$

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

$2 x (4 x + 3) + 3 (4 x + 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 3$ .

$(4 x + 3) (2 x + 3)$

Factor 8x^2+18x+9

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