Factor 9x^2-27x+14

$9 x^{2} - 27 x + 14$

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 $a \cdot c = 9 \cdot 14 = 126$ and whose sum is $b = - 27$ .

Factor $- 27$ out of $- 27 x$ .

$9 x^{2} - 27 (x) + 14$

Rewrite $- 27$ as $- 6$ plus $- 21$

$9 x^{2} + (- 6 - 21) x + 14$

Apply the distributive property.

$9 x^{2} - 6 x - 21 x + 14$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 x^{2} - 6 x) - 21 x + 14$

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

$3 x (3 x - 2) - 7 (3 x - 2)$

Step 3

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

$(3 x - 2) (3 x - 7)$

Factor 9x^2-27x+14

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