Factor 8y^2+17y+9

$8 y^{2} + 17 y + 9$

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 $b = 17$ .

Factor $17$ out of $17 y$ .

$8 y^{2} + 17 (y) + 9$

Rewrite $17$ as $8$ plus $9$

$8 y^{2} + (8 + 9) y + 9$

Apply the distributive property.

$8 y^{2} + 8 y + 9 y + 9$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 y^{2} + 8 y) + 9 y + 9$

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

$8 y (y + 1) + 9 (y + 1)$

Step 3

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

$(y + 1) (8 y + 9)$

Factor 8y^2+17y+9

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