Factor 2x^2-9x+7

$2 x^{2} - 9 x + 7$

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 $a \cdot c = 2 \cdot 7 = 14$ and whose sum is $b = - 9$ .

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

$2 x^{2} - 9 (x) + 7$

Rewrite $- 9$ as $- 2$ plus $- 7$

$2 x^{2} + (- 2 - 7) x + 7$

Apply the distributive property.

$2 x^{2} - 2 x - 7 x + 7$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 2 x) - 7 x + 7$

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

$2 x (x - 1) - 7 (x - 1)$

Step 3

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

$(x - 1) (2 x - 7)$

Factor 2x^2-9x+7

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