Factor 9x^2-9x+2

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

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

Factor $- 9$ out of $- 9 x$ .

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$3 x (3 x - 1) - 2 (3 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

$(3 x - 1) (3 x - 2)$

Factor 9x^2-9x+2

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