Factor 2b^2-9b+9

$2 b^{2} - 9 b + 9$

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 $a \cdot c = 2 \cdot 9 = 18$ and whose sum is $b = - 9$ .

Factor $- 9$ out of $- 9 b$ .

$2 b^{2} - 9 (b) + 9$

Rewrite $- 9$ as $- 3$ plus $- 6$

$2 b^{2} + (- 3 - 6) b + 9$

Apply the distributive property.

$2 b^{2} - 3 b - 6 b + 9$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 b^{2} - 3 b) - 6 b + 9$

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

$b (2 b - 3) - 3 (2 b - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 b - 3$ .

$(2 b - 3) (b - 3)$

Factor 2b^2-9b+9

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